Prepare_term-def_dataset.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "12731ec6-7bac-4d7a-8530-eb49ba20aa67",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8caa8cad-0822-4459-b560-a69d56087bbe",
   "metadata": {},
   "source": [
    "# Extract /textit{} contents from .tex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c9c8a6b0-5459-4457-beb3-4efdcf5e33fc",
   "metadata": {},
   "outputs": [],
   "source": [
    "import csv, re"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6072095d-9b12-4b68-8f6a-6cd7a6218cde",
   "metadata": {},
   "outputs": [],
   "source": [
    "import os"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "506b00ac-bd4f-4efb-8fbf-62047ff8608e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def extract_textit_sentence(tex_file, csv_file):\n",
    "    with open(tex_file, 'r',  errors='replace') as f:\n",
    "        tex = f.read()\n",
    "    if tex:\n",
    "        doc = tex.split(\"begin{document}\")\n",
    "        if (len(doc) >= 2) :\n",
    "            matches = re.findall(r'([^.]*?\\\\textit\\{([^}]*)\\}[^.]*\\.)', doc[1])\n",
    "            with open(csv_file, 'a') as csvfile:\n",
    "                writer = csv.writer(csvfile, delimiter=',')\n",
    "                for match in matches:\n",
    "                    sentence, textit_content = match\n",
    "                    writer.writerow([textit_content, sentence, tex_file])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2caa8b36-d811-4191-99f6-0283b9a3aaf1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# try with a single local tex file\n",
    "with open(\"output_1501.00565.csv\", 'w') as csvfile:\n",
    "        writer = csv.writer(csvfile, delimiter=',')\n",
    "        writer.writerow([\"textit_content\", \"sentence\", \"file_name\"])\n",
    "extract_textit_sentence('sampled_data/que_tex/1501.00565.tex', 'output_1501.00565.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "36df40cf-cfe2-43fa-b1ed-4721ee54f9e8",
   "metadata": {},
   "outputs": [],
   "source": [
    "with open(\"textit_sent_file.csv\", 'w') as csvfile:\n",
    "        writer = csv.writer(csvfile, delimiter=',')\n",
    "        writer.writerow([\"textit_content\", \"sentence\", \"file_name\"])\n",
    "tex_dir = '/home/shufan/Projects/def_arxiv/sampled_data/que_tex'\n",
    "for subdir, dirs, filenames in os.walk(tex_dir):\n",
    "    for filename in filenames:\n",
    "        filepath = \"sampled_data/que_tex/\" + filename\n",
    "        try:\n",
    "            extract_textit_sentence(filepath, 'textit_sent_file.csv')\n",
    "        except (UnicodeDecodeError) as error:\n",
    "            print(filepath + error.message)\n",
    "            continue\n",
    "        except (FileNotFoundError) as error:\n",
    "            print(filepath + \" NOT FOUND!!\")\n",
    "            continue\n",
    "            "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7d94a5fd-eb8e-4b32-a390-2d7f7ae362b5",
   "metadata": {},
   "outputs": [],
   "source": [
    "def extract_definitions(tex_file, csv_file):\n",
    "    with open(tex_file, 'r', errors='replace') as f:\n",
    "        tex_content = f.read()\n",
    "    doc = tex_content.split(\"begin{document}\")\n",
    "    if (len(doc) >= 2) :\n",
    "        doc = doc[1]\n",
    "        definitions = re.findall(r'\\\\begin{definition}\\[(.*?)](.*?)\\\\end{definition}', doc, re.DOTALL)\n",
    "        \n",
    "        theorem_sentences = re.findall(r'\\\\begin{theorem}(.*?)\\\\end{theorem}', doc, re.DOTALL)\n",
    "        thm_it_sentences = [sent for sent in theorem_sentences if '\\\\textit{' in sent]\n",
    "        thm_it_terms = [re.findall(r'\\\\textit{(.*?)}', sent) for sent in thm_it_sentences]\n",
    "        thm_emph_sentences = [sent for sent in theorem_sentences if '\\\\emph{' in sent]\n",
    "        thm_emph_terms = [re.findall(r'\\\\emph{(.*?)}', sent) for sent in thm_emph_sentences]\n",
    "        \n",
    "        def_sentences = re.findall(r'\\\\begin{definition}(.*?)\\\\end{definition}', doc, re.DOTALL)\n",
    "        def_it_sentences = [sent for sent in def_sentences if '\\\\textit{' in sent]\n",
    "        def_it_terms = [re.findall(r'\\\\textit{(.*?)}', sent) for sent in def_it_sentences]\n",
    "        def_emph_sentences = [sent for sent in def_sentences if '\\\\emph{' in sent]\n",
    "        def_emph_terms = [re.findall(r'\\\\emph{(.*?)}', sent) for sent in def_emph_sentences]\n",
    "        with open(csv_file, 'a') as csvfile:\n",
    "            writer = csv.writer(csvfile, delimiter=',')\n",
    "            for definition in definitions:\n",
    "                writer.writerow([definition[0].strip(), definition[1].strip(), tex_file, \"definition[]\"])\n",
    "            for sent, term_list in zip(thm_it_sentences, thm_it_terms):\n",
    "                writer.writerow([';'.join(term_list), sent, tex_file, \"theorem + \\\\textit{}\"])\n",
    "            for sent, term_list in zip(thm_emph_sentences, thm_emph_terms):\n",
    "                writer.writerow([';'.join(term_list), sent, tex_file, \"theorem + \\\\emph{}\"])\n",
    "            for sent, term_list in zip(def_it_sentences, def_it_terms):\n",
    "                writer.writerow([';'.join(term_list), sent, tex_file, \"definition + \\\\textit{}\"])\n",
    "            for sent, term_list in zip(def_emph_sentences, def_emph_terms):\n",
    "                writer.writerow([';'.join(term_list), sent, tex_file, \"definition + \\\\emph{}\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8ed8cb0a-46a0-47aa-992f-23acb973970a",
   "metadata": {},
   "outputs": [],
   "source": [
    "with open(\"output_def.csv\", 'w') as csvfile:\n",
    "        writer = csv.writer(csvfile, delimiter=',')\n",
    "        writer.writerow([\"term\", \"def\", \"file_name\", \"extraction_rule\"])\n",
    "extract_definitions('sampled_data/que_tex/paper_fullerenes-ipr.tex', 'output_def.csv')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "36de84cd-1996-4670-9924-0fa2276477f2",
   "metadata": {},
   "outputs": [],
   "source": [
    "with open(\"term_def_file.csv\", 'w') as csvfile:\n",
    "        writer = csv.writer(csvfile, delimiter=',')\n",
    "        writer.writerow([\"term\", \"def\", \"file_name\", \"extraction_rule\"])\n",
    "tex_dir = '/home/shufan/Projects/def_arxiv/sampled_data/que_tex'\n",
    "for subdir, dirs, filenames in os.walk(tex_dir):\n",
    "    for filename in filenames:\n",
    "        filepath = \"sampled_data/que_tex/\" + filename\n",
    "        try:\n",
    "            extract_definitions(filepath, 'term_def_file.csv')\n",
    "        except (UnicodeDecodeError) as error:\n",
    "            print(filepath + error.message)\n",
    "            continue\n",
    "        except (FileNotFoundError) as error:\n",
    "            print(filepath + \" NOT FOUND!!\")\n",
    "            continue"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ac497ac-a434-47dd-94a2-15a969350398",
   "metadata": {},
   "source": [
    "# Examine extracted term-def pairs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1078f144-10fa-48b9-a631-44a9f9fdefc0",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_all_def = pd.read_csv('out_def_all.csv', lineterminator='\\n', delimiter=',')\n",
    "df_all_def.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e77a7eeb-1584-4f87-ba58-d312ccb88a5b",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_all_def['extraction_rule\\r'].value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "25aac268-585c-424d-b964-ae6d58e04be8",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_all_def['term'].value_counts()[:60]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "490341b7-84b2-41b9-87ac-a04053a3e784",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean = df_all_def[~df_all_def['term'].isin([\"(i);(ii)\", \"i.e.\", '\\\\', \"not\", \"good\", \"(;)\", \"(i);(ii);(iii)\", \"\\\\textbf{Pr;\\\\textbf{Pr\", \"all\", \"type\", \"K\\\\\\\"{o\", \"et al.\", \"\\\\cite{AS17}\" ])]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "972c346f-962b-4534-a652-2baeb590eedf",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean = df_clean[ False  == df_clean[\"term\"].str.contains(\"cite{\") ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "88bf514f-e8a0-4855-b298-e4678edf156f",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean = df_clean[~df_clean['term'].isin([\"mod\", \"any\", \"\\\\\", \"\\d;\\d\" ])]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fedde476-b110-45b5-9a86-ceff209209bf",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean['term'].value_counts()[:60]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8f644c32-0cc2-4567-a045-30edccee8389",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean[df_clean['term'].str.len() == 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "906a35a6-a451-4c9e-ab83-16a03d715f1c",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean = df_clean[df_clean['term'].str.len() > 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b6392df0-86ad-4b10-bffc-87a5a49be012",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean['extraction_rule\\r'].value_counts()[:60]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "26058656-54d0-46dd-938e-91eae4398b41",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean.to_csv(\"cleaned_term_def.csv\", index=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4680b1c6-7682-4905-ab9f-ff3a2d5a3ca2",
   "metadata": {},
   "source": [
    "# Remove latex tags => convert latex into plain text"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d796130a-e3fd-4571-863d-136c1e299fe2",
   "metadata": {},
   "outputs": [],
   "source": [
    "#! pip install pylatexenc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "ca1003b4-276d-4a7a-8588-81894c13a656",
   "metadata": {},
   "outputs": [],
   "source": [
    "from pylatexenc.latex2text import LatexNodes2Text"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2fa0917b-17b4-4845-8fc4-a5b37fc74575",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean = pd.read_csv('cleaned_term_def.csv', lineterminator='\\n', delimiter=',')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "8be4a1ba-e0bd-4e2e-ae4d-1919af6b634c",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>term</th>\n",
       "      <th>def</th>\n",
       "      <th>file_name</th>\n",
       "      <th>extraction_rule\\r</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>admissible $G$-cover</td>\n",
       "      <td>\\label{def_admissibleGcover}\\nLet $G$ be a fin...</td>\n",
       "      <td>/home/shufan/que_tex/abelian_tropical_covers.tex</td>\n",
       "      <td>definition + \\emph{}\\r</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>$\\mathfrak{C} (S, k), \\text{ k-cut multi-set o...</td>\n",
       "      <td>%$$\\mathfrak{C} (S, k) = \\{\\pi(S): S \\subseteq...</td>\n",
       "      <td>/home/shufan/que_tex/CSPpaper.tex</td>\n",
       "      <td>definition[]\\r</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>$\\leq \\text{on graphs}$</td>\n",
       "      <td>\\begin{itemize}\\n$$$$\\n\\item Assign Graph G th...</td>\n",
       "      <td>/home/shufan/que_tex/CSPpaper.tex</td>\n",
       "      <td>definition[]\\r</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>light reduction pair;heavy reduction pair</td>\n",
       "      <td>\\n  Let $\\pi\\in\\fs_n$ and let $x,y$ be a pair ...</td>\n",
       "      <td>/home/shufan/que_tex/Post071005.tex</td>\n",
       "      <td>definition + \\emph{}\\r</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Testability for graph properties</td>\n",
       "      <td>\\label{testgraph}\\cite{RS}  A graph property $...</td>\n",
       "      <td>/home/shufan/que_tex/hereditary_submit.tex</td>\n",
       "      <td>definition[]\\r</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17851</th>\n",
       "      <td>Irreducibility</td>\n",
       "      <td>\\label{d:irred}\\nA matrix $A\\in\\Rpnn$ is calle...</td>\n",
       "      <td>/home/shufan/que_tex/1307.3716.tex</td>\n",
       "      <td>definition[]\\r</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17852</th>\n",
       "      <td>Transient of matrices</td>\n",
       "      <td>\\label{d:transient}\\nThe least nonnegative~$t$...</td>\n",
       "      <td>/home/shufan/que_tex/1307.3716.tex</td>\n",
       "      <td>definition[]\\r</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17853</th>\n",
       "      <td>Row and column transients</td>\n",
       "      <td>\\label{d:rowcolumn}\\nLet $A\\in\\Rpnn$.\\nThe lea...</td>\n",
       "      <td>/home/shufan/que_tex/1307.3716.tex</td>\n",
       "      <td>definition[]\\r</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17854</th>\n",
       "      <td>Factor rank in max algebra</td>\n",
       "      <td>In max algebra, {\\rm factor rank\\/} of $A\\in\\R...</td>\n",
       "      <td>/home/shufan/que_tex/1307.3716.tex</td>\n",
       "      <td>definition[]\\r</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17855</th>\n",
       "      <td>Visualization</td>\n",
       "      <td>\\label{d:visualize}\\nA matrix $A\\in\\Rpnn$ is c...</td>\n",
       "      <td>/home/shufan/que_tex/1307.3716.tex</td>\n",
       "      <td>definition[]\\r</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>17855 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                    term  \\\n",
       "0                                   admissible $G$-cover   \n",
       "1      $\\mathfrak{C} (S, k), \\text{ k-cut multi-set o...   \n",
       "2                                $\\leq \\text{on graphs}$   \n",
       "3              light reduction pair;heavy reduction pair   \n",
       "4                       Testability for graph properties   \n",
       "...                                                  ...   \n",
       "17851                                     Irreducibility   \n",
       "17852                              Transient of matrices   \n",
       "17853                          Row and column transients   \n",
       "17854                         Factor rank in max algebra   \n",
       "17855                                      Visualization   \n",
       "\n",
       "                                                     def  \\\n",
       "0      \\label{def_admissibleGcover}\\nLet $G$ be a fin...   \n",
       "1      %$$\\mathfrak{C} (S, k) = \\{\\pi(S): S \\subseteq...   \n",
       "2      \\begin{itemize}\\n$$$$\\n\\item Assign Graph G th...   \n",
       "3      \\n  Let $\\pi\\in\\fs_n$ and let $x,y$ be a pair ...   \n",
       "4      \\label{testgraph}\\cite{RS}  A graph property $...   \n",
       "...                                                  ...   \n",
       "17851  \\label{d:irred}\\nA matrix $A\\in\\Rpnn$ is calle...   \n",
       "17852  \\label{d:transient}\\nThe least nonnegative~$t$...   \n",
       "17853  \\label{d:rowcolumn}\\nLet $A\\in\\Rpnn$.\\nThe lea...   \n",
       "17854  In max algebra, {\\rm factor rank\\/} of $A\\in\\R...   \n",
       "17855  \\label{d:visualize}\\nA matrix $A\\in\\Rpnn$ is c...   \n",
       "\n",
       "                                              file_name  \\\n",
       "0      /home/shufan/que_tex/abelian_tropical_covers.tex   \n",
       "1                     /home/shufan/que_tex/CSPpaper.tex   \n",
       "2                     /home/shufan/que_tex/CSPpaper.tex   \n",
       "3                   /home/shufan/que_tex/Post071005.tex   \n",
       "4            /home/shufan/que_tex/hereditary_submit.tex   \n",
       "...                                                 ...   \n",
       "17851                /home/shufan/que_tex/1307.3716.tex   \n",
       "17852                /home/shufan/que_tex/1307.3716.tex   \n",
       "17853                /home/shufan/que_tex/1307.3716.tex   \n",
       "17854                /home/shufan/que_tex/1307.3716.tex   \n",
       "17855                /home/shufan/que_tex/1307.3716.tex   \n",
       "\n",
       "            extraction_rule\\r  \n",
       "0      definition + \\emph{}\\r  \n",
       "1              definition[]\\r  \n",
       "2              definition[]\\r  \n",
       "3      definition + \\emph{}\\r  \n",
       "4              definition[]\\r  \n",
       "...                       ...  \n",
       "17851          definition[]\\r  \n",
       "17852          definition[]\\r  \n",
       "17853          definition[]\\r  \n",
       "17854          definition[]\\r  \n",
       "17855          definition[]\\r  \n",
       "\n",
       "[17855 rows x 4 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_clean.dropna(\n",
    "    axis=0,\n",
    "    how='any', #drop all rows with just a empty cell(s)\n",
    "    inplace=True\n",
    ")\n",
    "\n",
    "df_clean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "2da6d993-b49e-4872-a6eb-426a81189b01",
   "metadata": {},
   "outputs": [],
   "source": [
    "def insert_space_before_and_after_emph_or_textit(s):\n",
    "    # insert_space_after_brace\n",
    "    after_pattern = r'(\\\\(?:emph|textit)\\{[^}]*\\})([.,;)\\]]|$)'\n",
    "    \n",
    "    # Use the re.sub function to insert a space after } for all matching substrings\n",
    "    result = re.sub(after_pattern, r'\\1 \\2', s)\n",
    "    \n",
    "    # insert_space_after_parenthesis_or_bracket(s) :\n",
    "    before_pattern = r'(\\(|\\[)(\\\\(?:emph|textit)\\{)'\n",
    "    \n",
    "    # Use the re.sub function to insert a space after ( or [ for all matching substrings\n",
    "    result = re.sub(before_pattern, r'\\1 \\2', result)\n",
    "    \n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "4d2d4be6-1a1c-4131-a3e6-ea0dfb09c83b",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean['def'] = df_clean['def'].apply(insert_space_before_and_after_emph_or_textit)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "411c9ded-89fd-4a52-87ca-5b6535045157",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean['plain_text_def'] = df_clean['def'].apply(LatexNodes2Text().latex_to_text)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "308bf491-bbc9-4a1f-b878-d477660e47a8",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: Error in configuration: macro '\\frac' failed its substitution!\n"
     ]
    }
   ],
   "source": [
    "df_clean['plain_text_term'] = df_clean['term'].apply(LatexNodes2Text().latex_to_text)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "3b0373b3-adb8-4949-9e70-a5b61c87ccf3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\\n\\n                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            106\n",
       "\\n                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               40\n",
       "\\n\\n\\n\\n                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         34\n",
       "\\n\\n\\n                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           30\n",
       "\\n\\n\\n\\n\\n\\n                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     23\n",
       "\\n\\n\\n\\n\\n\\n\\n                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   20\n",
       "\\n\\n\\n\\n\\n                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       19\n",
       "\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             15\n",
       "\\n\\n\\n\\n\\n\\n\\n\\n                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 14\n",
       " \\n\\n                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            13\n",
       "\\n\\n\\n\\n\\n\\n\\n\\n\\n                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               10\n",
       "\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            7\n",
       "\\n<cit.>, <cit.> A greedoid is a pair\\n(V,ℱ), where ℱ⊆2^V is a non-empty set system\\nsatisfying the following conditions:\\n\\nAccessibility: for every non-empty X∈ℱ there is an x∈\\nX such that X-{x}∈ℱ;\\n\\nExchange: for X,Y∈ℱ,| X| =|\\nY| +1, there is an x∈ X-Y such that Y∪{x}∈ℱ.\\n                                                                                                                                                                                                                                                                           6\n",
       "\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      6\n",
       "\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            5\n",
       "\\n\\nA partial matching in a poset P is a partial matching in the underlying graph of the Hasse diagram\\nof P, i.e., it is a subset M⊆ P × P such that\\n\\n\\n  * (a,b)∈ M implies b ≻ a; i.e. a<b and no c satisifies a<c<b.\\n\\n  * each a∈ P belongs to at most one element in M.\\n\\nWhen (a,b) ∈ M, we write a=d(b) and b=u(a).\\n\\n  * A partial matching on P is called acyclic if there does not exist a cycle\\n\\n    a_1 ≺ u(a_1) ≻ a_2 ≺ u(a_2) ≻⋯≺ u(a_m) ≻ a_1\\n\\nwith m≥ 2 and all a_i∈ P being distinct.\\n\\n                                              4\n",
       "\\n  If P is a (3+1)-free poset, then for each compatible listing (X_1, X_2, …, X_r+s) of its clone sets and tangles, we can obtain a word in Σ^* by replacing each clone set at level i by the letter c_i and each tangle straddling levels {i, i+1} by the letter t_i i+1.\\nIt can be seen that any two compatible listings for P are related by a sequence of valid swaps, so the set of these words is an equivalence class under the commutation relations for M (see, e.g. , <cit.>), and the corresponding element of M is called the skeleton of P.\\n      4\n",
       "\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          4\n",
       "\\n\\nA family  of permutations of V(H) is pairwise suitable for a hypergraph H if, for every two disjoint edges e,f ∈ E(H), there exists a permutation σ∈  which separates e and f. The cardinality of a smallest family of permutations that is pairwise suitable for H is called the separation dimension of H and is denoted by (H). \\n                                                                                                                                                                                                                         4\n",
       "\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n\\n                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  3\n",
       "Name: plain_text_def, dtype: int64"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_clean['plain_text_def'].value_counts()[:20]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "166783bb-f2c7-437c-8ff1-e9c7b150fae8",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Remove rows where 'def' contains only '\\n' or repeated '\\n'\n",
    "df_clean = df_clean[~df_clean['plain_text_def'].str.match(r'^\\n+$')]\n",
    "df_clean = df_clean[~df_clean['plain_text_def'].str.match(r'^ \\n+$')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "340191c1-9bdc-4ee6-b465-c8a8c316bea3",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean['plain_text_def'].value_counts()[:20]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "43b3ea43-7f63-4237-b8f2-673dc28b38d1",
   "metadata": {},
   "source": [
    "# Annotate definitions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "8fd0dad2-fa28-4ba8-920d-f27eb83c2a65",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean.rename(columns={\"extraction_rule\\r\": \"extraction_rule\"}, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "09d41239-8168-4af0-b7db-9f569e184e72",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean['extraction_rule'] = df_clean['extraction_rule'].str.rstrip('\\r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "1e3486c6-361c-4732-a0e7-019df0f96a2d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This is some text with B_MATH_TERM I_MATH_TERM I_MATH_TERM I_MATH_TERM I_MATH_TERM I_MATH_TERM in it. B_MATH_TERM. B_MATH_TERM I_MATH_TERM\n"
     ]
    }
   ],
   "source": [
    "def mask_emph(text):\n",
    "    pattern = r'\\\\emph\\{(.*?)\\}'\n",
    "\n",
    "    def replace(match):\n",
    "        words = match.group(1).split()\n",
    "        if not words:\n",
    "            return ''\n",
    "        masked_words = ['B_MATH_TERM'] + ['I_MATH_TERM'] * (len(words) - 1)\n",
    "        return ' '.join(masked_words)\n",
    "    return re.sub(pattern, replace, text)\n",
    "\n",
    "# Example usage\n",
    "text = r'This is some text with \\emph{emphasized words A B C D} in it. \\emph{blah}. \\emph{blah blah}'\n",
    "masked_text = mask_emph(text)\n",
    "print(masked_text)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "c6b6dcd8-5259-4110-ba44-d474a1996800",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B_MATH_TERM I_MATH_TERM! This is some text with B_MATH_TERM I_MATH_TERM I_MATH_TERM I_MATH_TERM I_MATH_TERM I_MATH_TERM in it. B_MATH_TERM. B_MATH_TERM I_MATH_TERM\n"
     ]
    }
   ],
   "source": [
    "def mask_textit(text):\n",
    "    pattern = r'\\\\textit\\{(.*?)\\}'\n",
    "\n",
    "    def replace(match):\n",
    "        words = match.group(1).split()\n",
    "        if not words:\n",
    "            return ''\n",
    "        masked_words = ['B_MATH_TERM'] + ['I_MATH_TERM'] * (len(words) - 1)\n",
    "        return ' '.join(masked_words)\n",
    "    return re.sub(pattern, replace, text)\n",
    "\n",
    "# Example usage\n",
    "text = r'\\textit{blah blah}! This is some text with \\textit{emphasized words A B C D} in it. \\textit{blah}. \\textit{blah blah}'\n",
    "masked_text = mask_textit(text)\n",
    "print(masked_text)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "942d3aec-9e44-4619-9dfe-1647cac3dcee",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This is some text with a B_MATH_TERM I_MATH_TERM in it. B_MATH_TERM I_MATH_TERM comes again.\n"
     ]
    }
   ],
   "source": [
    "def mask_substring(text, substring):\n",
    "    pattern = re.compile(re.escape(substring), re.IGNORECASE)\n",
    "    def replace(match):\n",
    "        words = match.group().split()\n",
    "        if not words:\n",
    "            return ''\n",
    "        masked_words = ['B_MATH_TERM'] + ['I_MATH_TERM'] * (len(words) - 1)\n",
    "        return ' '.join(masked_words)\n",
    "    return pattern.sub(replace, text)\n",
    "\n",
    "# Example usage\n",
    "text = 'This is some text with a SubString A in it. SubString A comes again.'\n",
    "substring = 'substring a'\n",
    "masked_text = mask_substring(text, substring)\n",
    "print(masked_text)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "45e73571-fc85-4b25-8871-973a6c57dbce",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "O O O O O B_MATH_TERM O O I_MATH_TERM O O\n"
     ]
    }
   ],
   "source": [
    "def label_text(text):\n",
    "    words = text.split()\n",
    "    masked_words = ['O' if word not in ('B_MATH_TERM', 'I_MATH_TERM') else word for word in words]\n",
    "    return ' '.join(masked_words)\n",
    "\n",
    "'''\n",
    "def label_text(text):\n",
    "    B_MASK = \"B_MATH_TERM\"\n",
    "    I_MASK = \"I_MATH_TERM\"\n",
    "    text = text.replace(B_MASK, f\" {B_MASK} \")\n",
    "    text = text.replace(I_MASK, f\" {I_MASK} \")\n",
    "    words = text.split()\n",
    "    masked_words = ['O' if word not in ('B_MATH_TERM', 'I_MATH_TERM') else word for word in words]\n",
    "    return ' '.join(masked_words)\n",
    "\n",
    "'''\n",
    "\n",
    "'''def label_text(text):\n",
    "    words = text.split()\n",
    "    masked_words = []\n",
    "    for word in words:\n",
    "        if word.contains('B_MATH_TERM'):\n",
    "            masked_words.append('B_MATH_TERM')\n",
    "        elif word.contains('I_MATH_TERM'):\n",
    "            masked_words.append('B_MATH_TERM')\n",
    "        else:\n",
    "            masked_words.append('O')\n",
    "    return ' '.join(masked_words)'''\n",
    "\n",
    "# Example usage\n",
    "text = 'This is some text with B_MATH_TERM , and I_MATH_TERM in it.'\n",
    "labeled_text = label_text(text)\n",
    "print(labeled_text)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "46fec228-dc06-4e88-862c-24f578e9d949",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O'"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Normally this should be corrected by previous space adding.\n",
    "text2 = 'If G has the property that, for any two edges {a, b},{c, d}, there is an automorphism α such that α(a) = c and α(b) = d and also an automorphism β such that β(a) = d and β(b) = c, then G is said to be B_MATH_TERM.'\n",
    "label_text(text2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "c1b6e32e-2e30-4592-b4d2-c9957d89c556",
   "metadata": {},
   "outputs": [],
   "source": [
    "def mask_def_sentence(sent, extraction_rule, term=''):\n",
    "    if 'emph' in extraction_rule:\n",
    "        masked_text = mask_emph(sent)\n",
    "    elif 'textit' in extraction_rule:\n",
    "        masked_text = mask_textit(sent)\n",
    "    else:\n",
    "        masked_text = mask_substring(sent, term)\n",
    "    return LatexNodes2Text().latex_to_text(masked_text) # convert to plain text"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "af07ee31-a38f-451d-a0b0-3591e1226230",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean['masked_plain_text_def'] = df_clean.apply(lambda x: mask_def_sentence(x['def'], x['extraction_rule'], x['term']), axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d57237b1-cc87-4cde-8dd6-eaf0b68b768a",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean['masked_plain_text_def'].loc[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "66dd79ed-272a-4359-931f-43947e39a314",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean[~df_clean['masked_plain_text_def'].str.contains('B_MATH_TERM')].to_csv(\"cleaned_term_def_but_unlabeled.csv\", index=False)\n",
    "# some definitions might be commented TODO: analyse the rest cases\n",
    "# most of this comes from the definitition[]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "9edcdf12-3d5c-4f56-bc01-40a5d800c271",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "definition[]              2006\n",
       "definition + \\emph{}       124\n",
       "theorem + \\emph{}           31\n",
       "definition + \\textit{}      19\n",
       "theorem + \\textit{}          5\n",
       "Name: extraction_rule, dtype: int64"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_unlabeled = df_clean[~df_clean['masked_plain_text_def'].str.contains('B_MATH_TERM')]\n",
    "df_unlabeled['extraction_rule'].value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "a2f6341e-65d9-44c6-9878-426c44268e1c",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean = df_clean[df_clean['masked_plain_text_def'].str.contains('B_MATH_TERM')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "f32d3aa3-c06a-47cb-95d5-a4096b797a6f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "definition + \\emph{}      10991\n",
       "definition + \\textit{}     1920\n",
       "definition[]               1333\n",
       "theorem + \\emph{}           886\n",
       "theorem + \\textit{}         157\n",
       "Name: extraction_rule, dtype: int64"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_clean['extraction_rule'].value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "5def39af-1de3-4442-8420-691a79140b1d",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean['labeled_def'] = df_clean['masked_plain_text_def'].apply(label_text)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "813c12bf-a8df-4c4c-bbd9-d1a21e12deff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "                                       52\n",
       "equivalent                             31\n",
       "<cit.>                                 20\n",
       "admissible                             20\n",
       "balanced                               20\n",
       "weight                                 20\n",
       "regular                                18\n",
       "compatible                             18\n",
       "simple                                 16\n",
       "minimal                                14\n",
       "connected                              13\n",
       "                                       13\n",
       "composition                            13\n",
       "rank                                   12\n",
       "isomorphic                             12\n",
       "symmetric                              12\n",
       "dual                                   12\n",
       "(<ref>                                 11\n",
       "critical                               11\n",
       "complete                               10\n",
       "pure                                   10\n",
       "degree                                 10\n",
       "stable                                 10\n",
       "closure                                10\n",
       "path                                   10\n",
       "prime                                  10\n",
       "normal                                  9\n",
       "irreducible                             9\n",
       "acyclic                                 9\n",
       "Tutte polynomial                        9\n",
       "special                                 9\n",
       "wep                                     9\n",
       "depth                                   9\n",
       "signature                               9\n",
       "restriction                             8\n",
       "split                                   8\n",
       "area word                               8\n",
       "maximal                                 8\n",
       "a.a.s.                                  8\n",
       "monotone                                8\n",
       "density                                 8\n",
       "shape                                   8\n",
       "linked                                  8\n",
       "reduced                                 8\n",
       "(<cit.>                                 8\n",
       "Schur function                          8\n",
       "dependency graph                        8\n",
       "Cartesian product                       7\n",
       "essential                               7\n",
       "fundamental quasisymmetric function     7\n",
       "inversion                               7\n",
       "direct sum                              7\n",
       "alternating                             7\n",
       "circuit                                 7\n",
       "partition                               7\n",
       "contraction                             7\n",
       "line graph                              7\n",
       "level                                   7\n",
       "nice                                    7\n",
       "matroid                                 7\n",
       "Name: plain_text_term, dtype: int64"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_clean['plain_text_term'].value_counts()[:60]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8980b1b2-21c2-498d-9197-f106cba40835",
   "metadata": {},
   "source": [
    "# Continue to clean the dataset..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "936e783d-a83e-48c7-8e3f-f11b34f78d9d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
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       "    .dataframe thead th {\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>term</th>\n",
       "      <th>def</th>\n",
       "      <th>file_name</th>\n",
       "      <th>extraction_rule</th>\n",
       "      <th>plain_text_def</th>\n",
       "      <th>plain_text_term</th>\n",
       "      <th>masked_plain_text_def</th>\n",
       "      <th>labeled_def</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1386</th>\n",
       "      <td>(i) ;(ii)</td>\n",
       "      <td>\\n\\label{th11}If $G$ is a K\\\"{o}nig-Egerv\\'{a}...</td>\n",
       "      <td>/home/shufan/que_tex/1506.00255.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nIf G is a König-Egerváry graph, then\\n\\n(i) ...</td>\n",
       "      <td>(i) ;(ii)</td>\n",
       "      <td>\\nIf G is a König-Egerváry graph, then\\n\\nB_MA...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1911</th>\n",
       "      <td>(ii);(iii)</td>\n",
       "      <td>\\n\\label{CLDELPS}Let $X$ be a del Pezzo surfac...</td>\n",
       "      <td>/home/shufan/que_tex/One_Sing.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet X be a del Pezzo surface of degree d:=(X...</td>\n",
       "      <td>(ii);(iii)</td>\n",
       "      <td>\\nLet X be a del Pezzo surface of degree d:=(X...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3015</th>\n",
       "      <td>(i);(ii);(iii);(iv)</td>\n",
       "      <td>\\n\\label{th15}Let $\\Gamma\\subseteq\\Omega(G)$ a...</td>\n",
       "      <td>/home/shufan/que_tex/1512.01994.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet Γ⊆Ω(G) and ∅≠Γ^'⊆MaxCritIndep(G), be suc...</td>\n",
       "      <td>(i);(ii);(iii);(iv)</td>\n",
       "      <td>\\nLet Γ⊆Ω(G) and ∅≠Γ^'⊆MaxCritIndep(G), be suc...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3802</th>\n",
       "      <td>(i);(ii);(iii);(iv)</td>\n",
       "      <td>\\n\\label{th7}Let $G$ be a graph whose $\\mathrm...</td>\n",
       "      <td>/home/shufan/que_tex/1506.00249.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet G be a graph whose core(G) is a critical...</td>\n",
       "      <td>(i);(ii);(iii);(iv)</td>\n",
       "      <td>\\nLet G be a graph whose core(G) is a critical...</td>\n",
       "      <td>O O O O O O O O O O O O B_MATH_TERM O B_MATH_T...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3803</th>\n",
       "      <td>(i);(ii) ;(iii);(iv)</td>\n",
       "      <td>\\n\\label{perfect matching}If $\\Gamma\\subseteq\\...</td>\n",
       "      <td>/home/shufan/que_tex/1506.00249.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nIf Γ⊆Ω(  G) and\\n|\\n\\n⋃\\nΓ| +|\\n\\n⋂\\nΓ| =2α(...</td>\n",
       "      <td>(i);(ii) ;(iii);(iv)</td>\n",
       "      <td>\\nIf Γ⊆Ω(  G) and\\n|\\n\\n⋃\\nΓ| +|\\n\\n⋂\\nΓ| =2α(...</td>\n",
       "      <td>O O O O O O O O O O O O B_MATH_TERM O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4727</th>\n",
       "      <td>(i) ;(ii);(iii)</td>\n",
       "      <td>\\n\\label{th9}Let $A$ be a critical independent...</td>\n",
       "      <td>/home/shufan/que_tex/1102.1859.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet A be a critical independent set in a gra...</td>\n",
       "      <td>(i) ;(ii);(iii)</td>\n",
       "      <td>\\nLet A be a critical independent set in a gra...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O B_MATH_TER...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5697</th>\n",
       "      <td>(i);(ii);(iii);(iv);(v);(vi) ;(vii)</td>\n",
       "      <td>\\n\\label{Th33}Let $G$\\ be a graph. Then the fo...</td>\n",
       "      <td>/home/shufan/que_tex/1102.1138.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet G be a graph. Then the following asserti...</td>\n",
       "      <td>(i);(ii);(iii);(iv);(v);(vi) ;(vii)</td>\n",
       "      <td>\\nLet G be a graph. Then the following asserti...</td>\n",
       "      <td>O O O O O O O O O O O B_MATH_TERM O O O B_MATH...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5698</th>\n",
       "      <td>(i) ;(ii);(iii)</td>\n",
       "      <td>\\n\\cite{Ore55}\\label{th1} Let $G=\\left(  A,B,E...</td>\n",
       "      <td>/home/shufan/que_tex/1102.1138.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n&lt;cit.&gt; Let G=(  A,B,E). Then the following a...</td>\n",
       "      <td>(i) ;(ii);(iii)</td>\n",
       "      <td>\\n&lt;cit.&gt; Let G=(  A,B,E). Then the following a...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5699</th>\n",
       "      <td>(i) ;(ii) ;(iii);(iv);(v)</td>\n",
       "      <td>\\n\\label{Th4}Let $G=\\left(  A,B,E\\right)  $ be...</td>\n",
       "      <td>/home/shufan/que_tex/1102.1138.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet G=(  A,B,E) be a bipartite graph. Then t...</td>\n",
       "      <td>(i) ;(ii) ;(iii);(iv);(v)</td>\n",
       "      <td>\\nLet G=(  A,B,E) be a bipartite graph. Then t...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5700</th>\n",
       "      <td>(i) ;(ii);(iii)</td>\n",
       "      <td>\\n\\label{th9}Let $X$ be a critical independent...</td>\n",
       "      <td>/home/shufan/que_tex/1102.1138.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet X be a critical independent set in a gra...</td>\n",
       "      <td>(i) ;(ii);(iii)</td>\n",
       "      <td>\\nLet X be a critical independent set in a gra...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O B_MATH_TER...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5701</th>\n",
       "      <td>(i);(ii) ;(iii)</td>\n",
       "      <td>\\n\\label{th11}If $G$ is a K\\\"{o}nig-Egerv\\'{a}...</td>\n",
       "      <td>/home/shufan/que_tex/1102.1138.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nIf G is a König-Egerváry graph, then\\n\\n(i)|...</td>\n",
       "      <td>(i);(ii) ;(iii)</td>\n",
       "      <td>\\nIf G is a König-Egerváry graph, then\\n\\nB_MA...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5702</th>\n",
       "      <td>(i) ;(ii) ;(iii) ;(iv)</td>\n",
       "      <td>\\nLet $G=\\left(  A,B,E\\right)  $ be a bipartit...</td>\n",
       "      <td>/home/shufan/que_tex/1102.1138.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet G=(  A,B,E) be a bipartite graph. Then t...</td>\n",
       "      <td>(i) ;(ii) ;(iii) ;(iv)</td>\n",
       "      <td>\\nLet G=(  A,B,E) be a bipartite graph. Then t...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6156</th>\n",
       "      <td>(i) ;(ii);(iii)</td>\n",
       "      <td>\\n\\cite{Levman2011d}\\label{th12} Let $G$ be a ...</td>\n",
       "      <td>/home/shufan/que_tex/1108.3756.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n&lt;cit.&gt; Let G be a unicyclic\\nnon-König-Egerv...</td>\n",
       "      <td>(i) ;(ii);(iii)</td>\n",
       "      <td>\\n&lt;cit.&gt; Let G be a unicyclic\\nnon-König-Egerv...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7300</th>\n",
       "      <td>(i);(ii);(iii)</td>\n",
       "      <td>\\n\\label{prop1} For any graph $G$, the followi...</td>\n",
       "      <td>/home/shufan/que_tex/1905.09462.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n For any graph G, the following assertions a...</td>\n",
       "      <td>(i);(ii);(iii)</td>\n",
       "      <td>\\n For any graph G, the following assertions a...</td>\n",
       "      <td>O O O O O O O O O B_MATH_TERM O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7301</th>\n",
       "      <td>(i);(ii)</td>\n",
       "      <td>\\n\\label{th1} If $G$ is of a K\\\"{o}nig-Egerv\\'...</td>\n",
       "      <td>/home/shufan/que_tex/1905.09462.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n If G is of a König-Egerváry graph, then\\n\\n...</td>\n",
       "      <td>(i);(ii)</td>\n",
       "      <td>\\n If G is of a König-Egerváry graph, then\\n\\n...</td>\n",
       "      <td>O O O O O O O O B_MATH_TERM O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8011</th>\n",
       "      <td>(i);(ii) ;(iii)</td>\n",
       "      <td>\\n\\label{th11}For a graph $G$ the following as...</td>\n",
       "      <td>/home/shufan/que_tex/1102.0401.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nFor a graph G the following assertions are e...</td>\n",
       "      <td>(i);(ii) ;(iii)</td>\n",
       "      <td>\\nFor a graph G the following assertions are e...</td>\n",
       "      <td>O O O O O O O O O B_MATH_TERM O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8012</th>\n",
       "      <td>(i) ;(ii);(iii);(iv)</td>\n",
       "      <td>\\n\\label{th8}\\emph{(i) }\\cite{NemhTro} Each lo...</td>\n",
       "      <td>/home/shufan/que_tex/1102.0401.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n(i) &lt;cit.&gt; Each local maximum independent se...</td>\n",
       "      <td>(i) ;(ii);(iii);(iv)</td>\n",
       "      <td>\\nB_MATH_TERM&lt;cit.&gt; Each local maximum indepen...</td>\n",
       "      <td>O O O O O O O O O O O O O B_MATH_TERM O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8013</th>\n",
       "      <td>(i);(ii);(iii)</td>\n",
       "      <td>\\n\\label{th7}For a graph $G=(V,E)$ of order $n...</td>\n",
       "      <td>/home/shufan/que_tex/1102.0401.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nFor a graph G=(V,E) of order n, the followin...</td>\n",
       "      <td>(i);(ii);(iii)</td>\n",
       "      <td>\\nFor a graph G=(V,E) of order n, the followin...</td>\n",
       "      <td>O O O O O O O O O O O O B_MATH_TERM O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8094</th>\n",
       "      <td>(i);(ii);(iii) ;(iv)</td>\n",
       "      <td>\\n\\label{th88}\\emph{(i)} \\cite{FinHartNow} Let...</td>\n",
       "      <td>/home/shufan/que_tex/1102.1142.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n(i) &lt;cit.&gt; Let G be a connected graph of gir...</td>\n",
       "      <td>(i);(ii);(iii) ;(iv)</td>\n",
       "      <td>\\nB_MATH_TERM &lt;cit.&gt; Let G be a connected grap...</td>\n",
       "      <td>B_MATH_TERM O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8095</th>\n",
       "      <td>(i);(ii);(iii);(iv)</td>\n",
       "      <td>\\n\\label{th10}Let $G=X\\circ\\{H_{1},H_{2},...,H...</td>\n",
       "      <td>/home/shufan/que_tex/1102.1142.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet G=X∘{H_1,H_2,...,H_n}, where H_1\\n,H_2,....</td>\n",
       "      <td>(i);(ii);(iii);(iv)</td>\n",
       "      <td>\\nLet G=X∘{H_1,H_2,...,H_n}, where H_1\\n,H_2,....</td>\n",
       "      <td>O O O O O O O O B_MATH_TERM O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8096</th>\n",
       "      <td>(i);(ii);(iii);(iv);(v);(vi);(vii)</td>\n",
       "      <td>\\nLet $G$ be a very well-covered graph. Then t...</td>\n",
       "      <td>/home/shufan/que_tex/1102.1142.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet G be a very well-covered graph. Then the...</td>\n",
       "      <td>(i);(ii);(iii);(iv);(v);(vi);(vii)</td>\n",
       "      <td>\\nLet G be a very well-covered graph. Then the...</td>\n",
       "      <td>O O O O O O O O O O O O B_MATH_TERM O O O O B_...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8429</th>\n",
       "      <td>(iv)</td>\n",
       "      <td>\\label{defdiagram}\\n\\begin{enumerate}\\n\\item \\...</td>\n",
       "      <td>/home/shufan/que_tex/1404.1572.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\n\\n\\n  * Let n,m,l∈ℤ such that n≥ 2, 1≤ m≤ n....</td>\n",
       "      <td>(iv)</td>\n",
       "      <td>\\n\\n\\n  * Let n,m,l∈ℤ such that n≥ 2, 1≤ m≤ n....</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10932</th>\n",
       "      <td>(i);(ii);(iii);(iv)</td>\n",
       "      <td>\\n\\label{AS+}Let $k\\geq2,$ $n\\geq2k+3,$ and $G...</td>\n",
       "      <td>/home/shufan/que_tex/1410.2142.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet k≥2, n≥2k+3, and G be a graph of order n...</td>\n",
       "      <td>(i);(ii);(iii);(iv)</td>\n",
       "      <td>\\nLet k≥2, n≥2k+3, and G be a graph of order n...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11351</th>\n",
       "      <td>(ii)</td>\n",
       "      <td>\\label{thm:KingStrongest}\\nLet $\\lambda$ and $...</td>\n",
       "      <td>/home/shufan/que_tex/SL2Plethysms8+.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet λ and μ be distinct non-empty partitions...</td>\n",
       "      <td>(ii)</td>\n",
       "      <td>\\nLet λ and μ be distinct non-empty partitions...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11655</th>\n",
       "      <td>(i) ;(ii) ;(iii)</td>\n",
       "      <td>\\n\\label{tYu}Let $k\\geq1$ and $G\\in\\mathcal{G}...</td>\n",
       "      <td>/home/shufan/que_tex/1308.4341.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet k≥1 and G∈𝒢(  n)  .\\n\\n(i) if 2k+2≤ n&lt;( ...</td>\n",
       "      <td>(i) ;(ii) ;(iii)</td>\n",
       "      <td>\\nLet k≥1 and G∈𝒢(  n)  .\\n\\nB_MATH_TERMif 2k+...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11656</th>\n",
       "      <td>(i);(ii);(iii);(iv)</td>\n",
       "      <td>\\n\\label{AS+}Let $k\\geq2,$ $n\\geq2k+3,$ $G\\in\\...</td>\n",
       "      <td>/home/shufan/que_tex/1308.4341.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet k≥2, n≥2k+3, G∈𝒢(  n) and\\nδ(  G)  ≥ k. ...</td>\n",
       "      <td>(i);(ii);(iii);(iv)</td>\n",
       "      <td>\\nLet k≥2, n≥2k+3, G∈𝒢(  n) and\\nδ(  G)  ≥ k. ...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12906</th>\n",
       "      <td>(i);(ii);(iii);(iv)</td>\n",
       "      <td>\\n\\label{th4}For a graph $G$ of order $n\\geq2$...</td>\n",
       "      <td>/home/shufan/que_tex/1004.4804.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nFor a graph G of order n≥2 the following ass...</td>\n",
       "      <td>(i);(ii);(iii);(iv)</td>\n",
       "      <td>\\nFor a graph G of order n≥2 the following ass...</td>\n",
       "      <td>O O O O O O O O O O O O B_MATH_TERM O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13600</th>\n",
       "      <td>(i);(ii);(iii) ;(iv);(v)</td>\n",
       "      <td>\\n\\label{prop:two disjoint-matching}For every ...</td>\n",
       "      <td>/home/shufan/que_tex/1807.06914.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nFor every graph G, the following\\nassertions...</td>\n",
       "      <td>(i);(ii);(iii) ;(iv);(v)</td>\n",
       "      <td>\\nFor every graph G, the following\\nassertions...</td>\n",
       "      <td>O O O O O O O O O B_MATH_TERM O O O O O O O B_...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13601</th>\n",
       "      <td>(i) ;(ii)</td>\n",
       "      <td>\\n\\label{th1}Let $S\\in\\mathrm{Ind}\\left(  G\\ri...</td>\n",
       "      <td>/home/shufan/que_tex/1807.06914.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet S∈Ind(  G) and S⊆Shed(G), then\\n\\n(i) th...</td>\n",
       "      <td>(i) ;(ii)</td>\n",
       "      <td>\\nLet S∈Ind(  G) and S⊆Shed(G), then\\n\\nB_MATH...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13603</th>\n",
       "      <td>(i) ;(ii)</td>\n",
       "      <td>\\n\\cite{LevMan2012}\\label{th13} Let $G$ be a u...</td>\n",
       "      <td>/home/shufan/que_tex/1807.06914.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n&lt;cit.&gt; Let G be a unicyclic\\nnon-König-Egerv...</td>\n",
       "      <td>(i) ;(ii)</td>\n",
       "      <td>\\n&lt;cit.&gt; Let G be a unicyclic\\nnon-König-Egerv...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14190</th>\n",
       "      <td>(i);(ii);(iii)</td>\n",
       "      <td>\\n\\label{th1}For a graph $G=(V,E)$, the follow...</td>\n",
       "      <td>/home/shufan/que_tex/0911.4626.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nFor a graph G=(V,E), the following propertie...</td>\n",
       "      <td>(i);(ii);(iii)</td>\n",
       "      <td>\\nFor a graph G=(V,E), the following propertie...</td>\n",
       "      <td>O O O O O O O O O B_MATH_TERM O O O O O B_MATH...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14660</th>\n",
       "      <td>(i);(ii);(iii);(iv);(v)</td>\n",
       "      <td>\\label{th2_main}\\n\\looseness=-1 For the length...</td>\n",
       "      <td>/home/shufan/que_tex/1808.09301.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n=-1 For the length function ℓ_q(r,R) and for...</td>\n",
       "      <td>(i);(ii);(iii);(iv);(v)</td>\n",
       "      <td>\\n=-1 For the length function ℓ_q(r,R) and for...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14661</th>\n",
       "      <td>\\textbf{(i);\\textbf{(ii);\\textbf{(iii)</td>\n",
       "      <td>\\label{th3_main_geom}\\nLet $q=4$ or $q\\ge7$. L...</td>\n",
       "      <td>/home/shufan/que_tex/1808.09301.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet q=4 or q≥7. Let Υ≥1. Let Σ_ρ=(2ρ+1,q). L...</td>\n",
       "      <td>(i);(ii);(iii)</td>\n",
       "      <td>\\nLet q=4 or q≥7. Let Υ≥1. Let Σ_ρ=(2ρ+1,q). L...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15727</th>\n",
       "      <td>(i) ;(ii);(iii);(iv);(v);(vi);(vii)</td>\n",
       "      <td>\\n\\label{th1}For every graph $G$ having no iso...</td>\n",
       "      <td>/home/shufan/que_tex/1610.03972.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nFor every graph G having no isolated vertice...</td>\n",
       "      <td>(i) ;(ii);(iii);(iv);(v);(vi);(vii)</td>\n",
       "      <td>\\nFor every graph G having no isolated vertice...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16332</th>\n",
       "      <td>(i);(ii);(iii);(iv);(v);(vi)</td>\n",
       "      <td>\\n\\label{th5}For a graph $G$ the following sta...</td>\n",
       "      <td>/home/shufan/que_tex/0908.1313.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nFor a graph G the following statements are e...</td>\n",
       "      <td>(i);(ii);(iii);(iv);(v);(vi)</td>\n",
       "      <td>\\nFor a graph G the following statements are e...</td>\n",
       "      <td>O O O O O O O O O B_MATH_TERM O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16333</th>\n",
       "      <td>(i);(ii);(iii);(iv);(v)</td>\n",
       "      <td>\\nLet $G$ be a graph of girth $\\geq6$, which i...</td>\n",
       "      <td>/home/shufan/que_tex/0908.1313.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet G be a graph of girth ≥6, which is isomo...</td>\n",
       "      <td>(i);(ii);(iii);(iv);(v)</td>\n",
       "      <td>\\nLet G be a graph of girth ≥6, which is isomo...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O B_...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17272</th>\n",
       "      <td>(i) ;(ii)</td>\n",
       "      <td>\\n\\label{th13}If $G$ is a $\\lambda$-quasi-regu...</td>\n",
       "      <td>/home/shufan/que_tex/1612.03736.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nIf G is a λ-quasi-regularizable graph of ord...</td>\n",
       "      <td>(i) ;(ii)</td>\n",
       "      <td>\\nIf G is a λ-quasi-regularizable graph of ord...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17273</th>\n",
       "      <td>(i);(ii);(iii) ;(iv)\\</td>\n",
       "      <td>\\n\\label{th3}If $G$ is a connected $1$-well-co...</td>\n",
       "      <td>/home/shufan/que_tex/1612.03736.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nIf G is a connected 1-well-covered graph, | ...</td>\n",
       "      <td>(i);(ii);(iii) ;(iv)</td>\n",
       "      <td>\\nIf G is a connected 1-well-covered graph, | ...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O B_...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17274</th>\n",
       "      <td>(i);(ii);(iii);(iv) ;(v);(vi)</td>\n",
       "      <td>\\nLet $H$\\ be a connected graph. If $G=H\\circ ...</td>\n",
       "      <td>/home/shufan/que_tex/1612.03736.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet H be a connected graph. If G=H∘ K_2 and ...</td>\n",
       "      <td>(i);(ii);(iii);(iv) ;(v);(vi)</td>\n",
       "      <td>\\nLet H be a connected graph. If G=H∘ K_2 and ...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O B_MATH_TERM ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17360</th>\n",
       "      <td>(i) ;(ii);(iii)</td>\n",
       "      <td>\\n\\cite{LevMan2013a}\\label{th9} For a critical...</td>\n",
       "      <td>/home/shufan/que_tex/1407.7368.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n&lt;cit.&gt; For a critical independent set A in a...</td>\n",
       "      <td>(i) ;(ii);(iii)</td>\n",
       "      <td>\\n&lt;cit.&gt; For a critical independent set A in a...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O B_MATH_TERM ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17361</th>\n",
       "      <td>(i) ;(ii) ;(iii);(iv);(v)</td>\n",
       "      <td>\\n\\cite{LevMan2011b}\\label{Th4} Let $G=\\left( ...</td>\n",
       "      <td>/home/shufan/que_tex/1407.7368.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n&lt;cit.&gt; Let G=(  A,B,E) be a bipartite\\ngraph...</td>\n",
       "      <td>(i) ;(ii) ;(iii);(iv);(v)</td>\n",
       "      <td>\\n&lt;cit.&gt; Let G=(  A,B,E) be a bipartite\\ngraph...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17362</th>\n",
       "      <td>(i);(ii) ;(iii)</td>\n",
       "      <td>\\n\\label{th11}If $G$ is a K\\\"{o}nig-Egerv\\'{a}...</td>\n",
       "      <td>/home/shufan/que_tex/1407.7368.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nIf G is a König-Egerváry graph, then\\n\\n(i)|...</td>\n",
       "      <td>(i);(ii) ;(iii)</td>\n",
       "      <td>\\nIf G is a König-Egerváry graph, then\\n\\nB_MA...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17363</th>\n",
       "      <td>(i) ;(ii) ;(iii) ;(iv)</td>\n",
       "      <td>\\nLet $G=\\left(  A,B,E\\right)  $ be a bipartit...</td>\n",
       "      <td>/home/shufan/que_tex/1407.7368.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet G=(  A,B,E) be a bipartite graph. Then t...</td>\n",
       "      <td>(i) ;(ii) ;(iii) ;(iv)</td>\n",
       "      <td>\\nLet G=(  A,B,E) be a bipartite graph. Then t...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17663</th>\n",
       "      <td>(i);(ii);(iii);(iv)</td>\n",
       "      <td>\\label{theo:stirling_mode_further}\\nFix $\\thet...</td>\n",
       "      <td>/home/shufan/que_tex/stirling_numbers.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nFix θ&gt;0. The mode u_n(θ) of the Ewens distri...</td>\n",
       "      <td>(i);(ii);(iii);(iv)</td>\n",
       "      <td>\\nFix θ&gt;0. The mode u_n(θ) of the Ewens distri...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O B_MATH_TERM O ...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                         term  \\\n",
       "1386                               (i) ;(ii)    \n",
       "1911                               (ii);(iii)   \n",
       "3015                      (i);(ii);(iii);(iv)   \n",
       "3802                      (i);(ii);(iii);(iv)   \n",
       "3803                    (i);(ii) ;(iii);(iv)    \n",
       "4727                         (i) ;(ii);(iii)    \n",
       "5697      (i);(ii);(iii);(iv);(v);(vi) ;(vii)   \n",
       "5698                          (i) ;(ii);(iii)   \n",
       "5699                (i) ;(ii) ;(iii);(iv);(v)   \n",
       "5700                         (i) ;(ii);(iii)    \n",
       "5701                         (i);(ii) ;(iii)    \n",
       "5702                  (i) ;(ii) ;(iii) ;(iv)    \n",
       "6156                          (i) ;(ii);(iii)   \n",
       "7300                          (i);(ii);(iii)    \n",
       "7301                                (i);(ii)    \n",
       "8011                          (i);(ii) ;(iii)   \n",
       "8012                     (i) ;(ii);(iii);(iv)   \n",
       "8013                          (i);(ii);(iii)    \n",
       "8094                     (i);(ii);(iii) ;(iv)   \n",
       "8095                      (i);(ii);(iii);(iv)   \n",
       "8096       (i);(ii);(iii);(iv);(v);(vi);(vii)   \n",
       "8429                                     (iv)   \n",
       "10932                    (i);(ii);(iii);(iv)    \n",
       "11351                                    (ii)   \n",
       "11655                       (i) ;(ii) ;(iii)    \n",
       "11656                    (i);(ii);(iii);(iv)    \n",
       "12906                     (i);(ii);(iii);(iv)   \n",
       "13600                (i);(ii);(iii) ;(iv);(v)   \n",
       "13601                              (i) ;(ii)    \n",
       "13603                               (i) ;(ii)   \n",
       "14190                         (i);(ii);(iii)    \n",
       "14660                 (i);(ii);(iii);(iv);(v)   \n",
       "14661  \\textbf{(i);\\textbf{(ii);\\textbf{(iii)   \n",
       "15727     (i) ;(ii);(iii);(iv);(v);(vi);(vii)   \n",
       "16332            (i);(ii);(iii);(iv);(v);(vi)   \n",
       "16333                 (i);(ii);(iii);(iv);(v)   \n",
       "17272                              (i) ;(ii)    \n",
       "17273                  (i);(ii);(iii) ;(iv)\\    \n",
       "17274           (i);(ii);(iii);(iv) ;(v);(vi)   \n",
       "17360                        (i) ;(ii);(iii)    \n",
       "17361               (i) ;(ii) ;(iii);(iv);(v)   \n",
       "17362                        (i);(ii) ;(iii)    \n",
       "17363                 (i) ;(ii) ;(iii) ;(iv)    \n",
       "17663                     (i);(ii);(iii);(iv)   \n",
       "\n",
       "                                                     def  \\\n",
       "1386   \\n\\label{th11}If $G$ is a K\\\"{o}nig-Egerv\\'{a}...   \n",
       "1911   \\n\\label{CLDELPS}Let $X$ be a del Pezzo surfac...   \n",
       "3015   \\n\\label{th15}Let $\\Gamma\\subseteq\\Omega(G)$ a...   \n",
       "3802   \\n\\label{th7}Let $G$ be a graph whose $\\mathrm...   \n",
       "3803   \\n\\label{perfect matching}If $\\Gamma\\subseteq\\...   \n",
       "4727   \\n\\label{th9}Let $A$ be a critical independent...   \n",
       "5697   \\n\\label{Th33}Let $G$\\ be a graph. Then the fo...   \n",
       "5698   \\n\\cite{Ore55}\\label{th1} Let $G=\\left(  A,B,E...   \n",
       "5699   \\n\\label{Th4}Let $G=\\left(  A,B,E\\right)  $ be...   \n",
       "5700   \\n\\label{th9}Let $X$ be a critical independent...   \n",
       "5701   \\n\\label{th11}If $G$ is a K\\\"{o}nig-Egerv\\'{a}...   \n",
       "5702   \\nLet $G=\\left(  A,B,E\\right)  $ be a bipartit...   \n",
       "6156   \\n\\cite{Levman2011d}\\label{th12} Let $G$ be a ...   \n",
       "7300   \\n\\label{prop1} For any graph $G$, the followi...   \n",
       "7301   \\n\\label{th1} If $G$ is of a K\\\"{o}nig-Egerv\\'...   \n",
       "8011   \\n\\label{th11}For a graph $G$ the following as...   \n",
       "8012   \\n\\label{th8}\\emph{(i) }\\cite{NemhTro} Each lo...   \n",
       "8013   \\n\\label{th7}For a graph $G=(V,E)$ of order $n...   \n",
       "8094   \\n\\label{th88}\\emph{(i)} \\cite{FinHartNow} Let...   \n",
       "8095   \\n\\label{th10}Let $G=X\\circ\\{H_{1},H_{2},...,H...   \n",
       "8096   \\nLet $G$ be a very well-covered graph. Then t...   \n",
       "8429   \\label{defdiagram}\\n\\begin{enumerate}\\n\\item \\...   \n",
       "10932  \\n\\label{AS+}Let $k\\geq2,$ $n\\geq2k+3,$ and $G...   \n",
       "11351  \\label{thm:KingStrongest}\\nLet $\\lambda$ and $...   \n",
       "11655  \\n\\label{tYu}Let $k\\geq1$ and $G\\in\\mathcal{G}...   \n",
       "11656  \\n\\label{AS+}Let $k\\geq2,$ $n\\geq2k+3,$ $G\\in\\...   \n",
       "12906  \\n\\label{th4}For a graph $G$ of order $n\\geq2$...   \n",
       "13600  \\n\\label{prop:two disjoint-matching}For every ...   \n",
       "13601  \\n\\label{th1}Let $S\\in\\mathrm{Ind}\\left(  G\\ri...   \n",
       "13603  \\n\\cite{LevMan2012}\\label{th13} Let $G$ be a u...   \n",
       "14190  \\n\\label{th1}For a graph $G=(V,E)$, the follow...   \n",
       "14660  \\label{th2_main}\\n\\looseness=-1 For the length...   \n",
       "14661  \\label{th3_main_geom}\\nLet $q=4$ or $q\\ge7$. L...   \n",
       "15727  \\n\\label{th1}For every graph $G$ having no iso...   \n",
       "16332  \\n\\label{th5}For a graph $G$ the following sta...   \n",
       "16333  \\nLet $G$ be a graph of girth $\\geq6$, which i...   \n",
       "17272  \\n\\label{th13}If $G$ is a $\\lambda$-quasi-regu...   \n",
       "17273  \\n\\label{th3}If $G$ is a connected $1$-well-co...   \n",
       "17274  \\nLet $H$\\ be a connected graph. If $G=H\\circ ...   \n",
       "17360  \\n\\cite{LevMan2013a}\\label{th9} For a critical...   \n",
       "17361  \\n\\cite{LevMan2011b}\\label{Th4} Let $G=\\left( ...   \n",
       "17362  \\n\\label{th11}If $G$ is a K\\\"{o}nig-Egerv\\'{a}...   \n",
       "17363  \\nLet $G=\\left(  A,B,E\\right)  $ be a bipartit...   \n",
       "17663  \\label{theo:stirling_mode_further}\\nFix $\\thet...   \n",
       "\n",
       "                                       file_name       extraction_rule  \\\n",
       "1386         /home/shufan/que_tex/1506.00255.tex     theorem + \\emph{}   \n",
       "1911           /home/shufan/que_tex/One_Sing.tex     theorem + \\emph{}   \n",
       "3015         /home/shufan/que_tex/1512.01994.tex     theorem + \\emph{}   \n",
       "3802         /home/shufan/que_tex/1506.00249.tex     theorem + \\emph{}   \n",
       "3803         /home/shufan/que_tex/1506.00249.tex     theorem + \\emph{}   \n",
       "4727          /home/shufan/que_tex/1102.1859.tex     theorem + \\emph{}   \n",
       "5697          /home/shufan/que_tex/1102.1138.tex     theorem + \\emph{}   \n",
       "5698          /home/shufan/que_tex/1102.1138.tex     theorem + \\emph{}   \n",
       "5699          /home/shufan/que_tex/1102.1138.tex     theorem + \\emph{}   \n",
       "5700          /home/shufan/que_tex/1102.1138.tex     theorem + \\emph{}   \n",
       "5701          /home/shufan/que_tex/1102.1138.tex     theorem + \\emph{}   \n",
       "5702          /home/shufan/que_tex/1102.1138.tex     theorem + \\emph{}   \n",
       "6156          /home/shufan/que_tex/1108.3756.tex     theorem + \\emph{}   \n",
       "7300         /home/shufan/que_tex/1905.09462.tex     theorem + \\emph{}   \n",
       "7301         /home/shufan/que_tex/1905.09462.tex     theorem + \\emph{}   \n",
       "8011          /home/shufan/que_tex/1102.0401.tex     theorem + \\emph{}   \n",
       "8012          /home/shufan/que_tex/1102.0401.tex     theorem + \\emph{}   \n",
       "8013          /home/shufan/que_tex/1102.0401.tex     theorem + \\emph{}   \n",
       "8094          /home/shufan/que_tex/1102.1142.tex     theorem + \\emph{}   \n",
       "8095          /home/shufan/que_tex/1102.1142.tex     theorem + \\emph{}   \n",
       "8096          /home/shufan/que_tex/1102.1142.tex     theorem + \\emph{}   \n",
       "8429          /home/shufan/que_tex/1404.1572.tex  definition + \\emph{}   \n",
       "10932         /home/shufan/que_tex/1410.2142.tex     theorem + \\emph{}   \n",
       "11351    /home/shufan/que_tex/SL2Plethysms8+.tex     theorem + \\emph{}   \n",
       "11655         /home/shufan/que_tex/1308.4341.tex     theorem + \\emph{}   \n",
       "11656         /home/shufan/que_tex/1308.4341.tex     theorem + \\emph{}   \n",
       "12906         /home/shufan/que_tex/1004.4804.tex     theorem + \\emph{}   \n",
       "13600        /home/shufan/que_tex/1807.06914.tex     theorem + \\emph{}   \n",
       "13601        /home/shufan/que_tex/1807.06914.tex     theorem + \\emph{}   \n",
       "13603        /home/shufan/que_tex/1807.06914.tex     theorem + \\emph{}   \n",
       "14190         /home/shufan/que_tex/0911.4626.tex     theorem + \\emph{}   \n",
       "14660        /home/shufan/que_tex/1808.09301.tex     theorem + \\emph{}   \n",
       "14661        /home/shufan/que_tex/1808.09301.tex     theorem + \\emph{}   \n",
       "15727        /home/shufan/que_tex/1610.03972.tex     theorem + \\emph{}   \n",
       "16332         /home/shufan/que_tex/0908.1313.tex     theorem + \\emph{}   \n",
       "16333         /home/shufan/que_tex/0908.1313.tex     theorem + \\emph{}   \n",
       "17272        /home/shufan/que_tex/1612.03736.tex     theorem + \\emph{}   \n",
       "17273        /home/shufan/que_tex/1612.03736.tex     theorem + \\emph{}   \n",
       "17274        /home/shufan/que_tex/1612.03736.tex     theorem + \\emph{}   \n",
       "17360         /home/shufan/que_tex/1407.7368.tex     theorem + \\emph{}   \n",
       "17361         /home/shufan/que_tex/1407.7368.tex     theorem + \\emph{}   \n",
       "17362         /home/shufan/que_tex/1407.7368.tex     theorem + \\emph{}   \n",
       "17363         /home/shufan/que_tex/1407.7368.tex     theorem + \\emph{}   \n",
       "17663  /home/shufan/que_tex/stirling_numbers.tex     theorem + \\emph{}   \n",
       "\n",
       "                                          plain_text_def  \\\n",
       "1386   \\nIf G is a König-Egerváry graph, then\\n\\n(i) ...   \n",
       "1911   \\nLet X be a del Pezzo surface of degree d:=(X...   \n",
       "3015   \\nLet Γ⊆Ω(G) and ∅≠Γ^'⊆MaxCritIndep(G), be suc...   \n",
       "3802   \\nLet G be a graph whose core(G) is a critical...   \n",
       "3803   \\nIf Γ⊆Ω(  G) and\\n|\\n\\n⋃\\nΓ| +|\\n\\n⋂\\nΓ| =2α(...   \n",
       "4727   \\nLet A be a critical independent set in a gra...   \n",
       "5697   \\nLet G be a graph. Then the following asserti...   \n",
       "5698   \\n<cit.> Let G=(  A,B,E). Then the following a...   \n",
       "5699   \\nLet G=(  A,B,E) be a bipartite graph. Then t...   \n",
       "5700   \\nLet X be a critical independent set in a gra...   \n",
       "5701   \\nIf G is a König-Egerváry graph, then\\n\\n(i)|...   \n",
       "5702   \\nLet G=(  A,B,E) be a bipartite graph. Then t...   \n",
       "6156   \\n<cit.> Let G be a unicyclic\\nnon-König-Egerv...   \n",
       "7300   \\n For any graph G, the following assertions a...   \n",
       "7301   \\n If G is of a König-Egerváry graph, then\\n\\n...   \n",
       "8011   \\nFor a graph G the following assertions are e...   \n",
       "8012   \\n(i) <cit.> Each local maximum independent se...   \n",
       "8013   \\nFor a graph G=(V,E) of order n, the followin...   \n",
       "8094   \\n(i) <cit.> Let G be a connected graph of gir...   \n",
       "8095   \\nLet G=X∘{H_1,H_2,...,H_n}, where H_1\\n,H_2,....   \n",
       "8096   \\nLet G be a very well-covered graph. Then the...   \n",
       "8429   \\n\\n\\n  * Let n,m,l∈ℤ such that n≥ 2, 1≤ m≤ n....   \n",
       "10932  \\nLet k≥2, n≥2k+3, and G be a graph of order n...   \n",
       "11351  \\nLet λ and μ be distinct non-empty partitions...   \n",
       "11655  \\nLet k≥1 and G∈𝒢(  n)  .\\n\\n(i) if 2k+2≤ n<( ...   \n",
       "11656  \\nLet k≥2, n≥2k+3, G∈𝒢(  n) and\\nδ(  G)  ≥ k. ...   \n",
       "12906  \\nFor a graph G of order n≥2 the following ass...   \n",
       "13600  \\nFor every graph G, the following\\nassertions...   \n",
       "13601  \\nLet S∈Ind(  G) and S⊆Shed(G), then\\n\\n(i) th...   \n",
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       "14660  \\n=-1 For the length function ℓ_q(r,R) and for...   \n",
       "14661  \\nLet q=4 or q≥7. Let Υ≥1. Let Σ_ρ=(2ρ+1,q). L...   \n",
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       "17361  \\n<cit.> Let G=(  A,B,E) be a bipartite\\ngraph...   \n",
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       "8013                       (i);(ii);(iii)    \n",
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       "8095                   (i);(ii);(iii);(iv)   \n",
       "8096    (i);(ii);(iii);(iv);(v);(vi);(vii)   \n",
       "8429                                  (iv)   \n",
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       "11351                                 (ii)   \n",
       "11655                    (i) ;(ii) ;(iii)    \n",
       "11656                 (i);(ii);(iii);(iv)    \n",
       "12906                  (i);(ii);(iii);(iv)   \n",
       "13600             (i);(ii);(iii) ;(iv);(v)   \n",
       "13601                           (i) ;(ii)    \n",
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       "16333              (i);(ii);(iii);(iv);(v)   \n",
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       "\n",
       "                                   masked_plain_text_def  \\\n",
       "1386   \\nIf G is a König-Egerváry graph, then\\n\\nB_MA...   \n",
       "1911   \\nLet X be a del Pezzo surface of degree d:=(X...   \n",
       "3015   \\nLet Γ⊆Ω(G) and ∅≠Γ^'⊆MaxCritIndep(G), be suc...   \n",
       "3802   \\nLet G be a graph whose core(G) is a critical...   \n",
       "3803   \\nIf Γ⊆Ω(  G) and\\n|\\n\\n⋃\\nΓ| +|\\n\\n⋂\\nΓ| =2α(...   \n",
       "4727   \\nLet A be a critical independent set in a gra...   \n",
       "5697   \\nLet G be a graph. Then the following asserti...   \n",
       "5698   \\n<cit.> Let G=(  A,B,E). Then the following a...   \n",
       "5699   \\nLet G=(  A,B,E) be a bipartite graph. Then t...   \n",
       "5700   \\nLet X be a critical independent set in a gra...   \n",
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       "5702   \\nLet G=(  A,B,E) be a bipartite graph. Then t...   \n",
       "6156   \\n<cit.> Let G be a unicyclic\\nnon-König-Egerv...   \n",
       "7300   \\n For any graph G, the following assertions a...   \n",
       "7301   \\n If G is of a König-Egerváry graph, then\\n\\n...   \n",
       "8011   \\nFor a graph G the following assertions are e...   \n",
       "8012   \\nB_MATH_TERM<cit.> Each local maximum indepen...   \n",
       "8013   \\nFor a graph G=(V,E) of order n, the followin...   \n",
       "8094   \\nB_MATH_TERM <cit.> Let G be a connected grap...   \n",
       "8095   \\nLet G=X∘{H_1,H_2,...,H_n}, where H_1\\n,H_2,....   \n",
       "8096   \\nLet G be a very well-covered graph. Then the...   \n",
       "8429   \\n\\n\\n  * Let n,m,l∈ℤ such that n≥ 2, 1≤ m≤ n....   \n",
       "10932  \\nLet k≥2, n≥2k+3, and G be a graph of order n...   \n",
       "11351  \\nLet λ and μ be distinct non-empty partitions...   \n",
       "11655  \\nLet k≥1 and G∈𝒢(  n)  .\\n\\nB_MATH_TERMif 2k+...   \n",
       "11656  \\nLet k≥2, n≥2k+3, G∈𝒢(  n) and\\nδ(  G)  ≥ k. ...   \n",
       "12906  \\nFor a graph G of order n≥2 the following ass...   \n",
       "13600  \\nFor every graph G, the following\\nassertions...   \n",
       "13601  \\nLet S∈Ind(  G) and S⊆Shed(G), then\\n\\nB_MATH...   \n",
       "13603  \\n<cit.> Let G be a unicyclic\\nnon-König-Egerv...   \n",
       "14190  \\nFor a graph G=(V,E), the following propertie...   \n",
       "14660  \\n=-1 For the length function ℓ_q(r,R) and for...   \n",
       "14661  \\nLet q=4 or q≥7. Let Υ≥1. Let Σ_ρ=(2ρ+1,q). L...   \n",
       "15727  \\nFor every graph G having no isolated vertice...   \n",
       "16332  \\nFor a graph G the following statements are e...   \n",
       "16333  \\nLet G be a graph of girth ≥6, which is isomo...   \n",
       "17272  \\nIf G is a λ-quasi-regularizable graph of ord...   \n",
       "17273  \\nIf G is a connected 1-well-covered graph, | ...   \n",
       "17274  \\nLet H be a connected graph. If G=H∘ K_2 and ...   \n",
       "17360  \\n<cit.> For a critical independent set A in a...   \n",
       "17361  \\n<cit.> Let G=(  A,B,E) be a bipartite\\ngraph...   \n",
       "17362  \\nIf G is a König-Egerváry graph, then\\n\\nB_MA...   \n",
       "17363  \\nLet G=(  A,B,E) be a bipartite graph. Then t...   \n",
       "17663  \\nFix θ>0. The mode u_n(θ) of the Ewens distri...   \n",
       "\n",
       "                                             labeled_def  \n",
       "1386       O O O O O O O O O O O O O O O O O O O O O O O  \n",
       "1911   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "3015   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "3802   O O O O O O O O O O O O B_MATH_TERM O B_MATH_T...  \n",
       "3803   O O O O O O O O O O O O B_MATH_TERM O O O O O ...  \n",
       "4727   O O O O O O O O O O O O O O O O O O B_MATH_TER...  \n",
       "5697   O O O O O O O O O O O B_MATH_TERM O O O B_MATH...  \n",
       "5698   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "5699   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "5700   O O O O O O O O O O O O O O O O O O B_MATH_TER...  \n",
       "5701   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "5702   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "6156   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "7300   O O O O O O O O O B_MATH_TERM O O O O O O O O ...  \n",
       "7301   O O O O O O O O B_MATH_TERM O O O O O O O O O ...  \n",
       "8011   O O O O O O O O O B_MATH_TERM O O O O O O O O ...  \n",
       "8012   O O O O O O O O O O O O O B_MATH_TERM O O O O ...  \n",
       "8013   O O O O O O O O O O O O B_MATH_TERM O O O O O ...  \n",
       "8094   B_MATH_TERM O O O O O O O O O O O O O O O O O ...  \n",
       "8095   O O O O O O O O B_MATH_TERM O O O O O O O O O ...  \n",
       "8096   O O O O O O O O O O O O B_MATH_TERM O O O O B_...  \n",
       "8429   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "10932  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "11351  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "11655  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "11656  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "12906  O O O O O O O O O O O O B_MATH_TERM O O O O O ...  \n",
       "13600  O O O O O O O O O B_MATH_TERM O O O O O O O B_...  \n",
       "13601  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "13603  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "14190  O O O O O O O O O B_MATH_TERM O O O O O B_MATH...  \n",
       "14660  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "14661  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "15727  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "16332  O O O O O O O O O B_MATH_TERM O O O O O O O O ...  \n",
       "16333  O O O O O O O O O O O O O O O O O O O O O O B_...  \n",
       "17272  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "17273  O O O O O O O O O O O O O O O O O O O O O O B_...  \n",
       "17274  O O O O O O O O O O O O O O O O O B_MATH_TERM ...  \n",
       "17360  O O O O O O O O O O O O O O O O O B_MATH_TERM ...  \n",
       "17361  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "17362  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "17363  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "17663  O O O O O O O O O O O O O O O O B_MATH_TERM O ...  "
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_clean[df_clean['plain_text_term'].str.match(r'^\\s*(\\([ivxlcdm]+\\)\\s*([,;]\\s*\\([ivxlcdm]+\\)\\s*)*)$')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "c5525733-58ed-401a-88bc-823acf694c11",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean = df_clean[~df_clean['plain_text_term'].str.match(r'^\\s*(\\([ivxlcdm]+\\)\\s*([,;]\\s*\\([ivxlcdm]+\\)\\s*)*)$')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "556349a3-0277-4ae5-9e08-f9465ae34959",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>term</th>\n",
       "      <th>def</th>\n",
       "      <th>file_name</th>\n",
       "      <th>extraction_rule</th>\n",
       "      <th>plain_text_def</th>\n",
       "      <th>plain_text_term</th>\n",
       "      <th>masked_plain_text_def</th>\n",
       "      <th>labeled_def</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>129</th>\n",
       "      <td>\\Csimple</td>\n",
       "      <td>Let $P$ be a polyhedron. We say $P$ is \\Csimpl...</td>\n",
       "      <td>/home/shufan/que_tex/oncircuits.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>Let P be a polyhedron. We say P is  if all cir...</td>\n",
       "      <td></td>\n",
       "      <td>Let P be a polyhedron. We say P is B_MATH_TERM...</td>\n",
       "      <td>O O O O O O O O O B_MATH_TERM O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1033</th>\n",
       "      <td>\\Cyclewidth</td>\n",
       "      <td>Let $D$ be a \\digraph.\\n\\t\\tA cycle decomposit...</td>\n",
       "      <td>/home/shufan/que_tex/bipgrid.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>Let D be a .\\n\\t\\tA cycle decomposition of D i...</td>\n",
       "      <td></td>\n",
       "      <td>Let D be a .\\n\\t\\tA cycle decomposition of D i...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1045</th>\n",
       "      <td>\\cycPoros</td>\n",
       "      <td>[\\Cyclewidth]\\n\\t\\tLet $D$ be a \\digraph.\\n\\t\\...</td>\n",
       "      <td>/home/shufan/que_tex/bipgrid.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>[]\\n\\t\\tLet D be a .\\n\\t\\tA cycle decompositio...</td>\n",
       "      <td></td>\n",
       "      <td>[]\\n\\t\\tLet D be a .\\n\\t\\tA cycle decompositio...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1047</th>\n",
       "      <td>\\matPoros</td>\n",
       "      <td>[matching-porosity]\\n\\t\\tLet $G$ be a matching...</td>\n",
       "      <td>/home/shufan/que_tex/bipgrid.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>[matching-porosity]\\n\\t\\tLet G be a matching c...</td>\n",
       "      <td></td>\n",
       "      <td>[matching-porosity]\\n\\t\\tLet G be a matching c...</td>\n",
       "      <td>O O O O O O O O O O O O O B_MATH_TERM O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1598</th>\n",
       "      <td>\\edg</td>\n",
       "      <td>[non-boundary edge classes]\\label{def:non-boun...</td>\n",
       "      <td>/home/shufan/que_tex/trilongest.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>[non-boundary edge classes] Let _π be an M-bou...</td>\n",
       "      <td></td>\n",
       "      <td>[non-boundary edge classes] Let _π be an M-bou...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1599</th>\n",
       "      <td>\\edg</td>\n",
       "      <td>[forward extension]\\label{def:forward-ext}\\nLe...</td>\n",
       "      <td>/home/shufan/que_tex/trilongest.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>[forward extension]\\nLet _π be an M-bounded tr...</td>\n",
       "      <td></td>\n",
       "      <td>[forward extension]\\nLet _π be an M-bounded tr...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2066</th>\n",
       "      <td>\\robust</td>\n",
       "      <td>Given two sets $A \\subseteq L$ and $B \\subsete...</td>\n",
       "      <td>/home/shufan/que_tex/eccc-arxiv.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>Given two sets A ⊆ L and B ⊆ R, we say that th...</td>\n",
       "      <td></td>\n",
       "      <td>Given two sets A ⊆ L and B ⊆ R, we say that th...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2127</th>\n",
       "      <td>$\\EK$</td>\n",
       "      <td>Let $\\K$ be a class of structures in $L_I := \\...</td>\n",
       "      <td>/home/shufan/que_tex/Sokic_Pawliuk_amenable_au...</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>Let  be a class of structures in L_I := {R_i :...</td>\n",
       "      <td></td>\n",
       "      <td>Let  be a class of structures in L_I := {R_i :...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2128</th>\n",
       "      <td>$\\LEK$</td>\n",
       "      <td>Let $L_I := \\{R_i : i \\in I\\}$ and $L_J := \\{R...</td>\n",
       "      <td>/home/shufan/que_tex/Sokic_Pawliuk_amenable_au...</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>Let L_I := {R_i : i ∈ I} and L_J := {R_j : j ∈...</td>\n",
       "      <td></td>\n",
       "      <td>Let L_I := {R_i : i ∈ I} and L_J := {R_j : j ∈...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2129</th>\n",
       "      <td>$\\QOPstar$</td>\n",
       "      <td>Let $(\\K,\\K^*)$ be an excellent pair. We say t...</td>\n",
       "      <td>/home/shufan/que_tex/Sokic_Pawliuk_amenable_au...</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>Let (,^*) be an excellent pair. We say that ^*...</td>\n",
       "      <td></td>\n",
       "      <td>Let (,^*) be an excellent pair. We say that ^*...</td>\n",
       "      <td>O O O O O O O O O O O O B_MATH_TERM O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2130</th>\n",
       "      <td>$\\QOP$</td>\n",
       "      <td>Let $(\\K,\\K^*)$ be an excellent pair. We say t...</td>\n",
       "      <td>/home/shufan/que_tex/Sokic_Pawliuk_amenable_au...</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>Let (,^*) be an excellent pair. We say that ^*...</td>\n",
       "      <td></td>\n",
       "      <td>Let (,^*) be an excellent pair. We say that ^*...</td>\n",
       "      <td>O O O O O O O O O O O O B_MATH_TERM O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2571</th>\n",
       "      <td>\\textsf{mnd</td>\n",
       "      <td>\\label{bhth}\\nConjecture \\ref{minmax} is true ...</td>\n",
       "      <td>/home/shufan/que_tex/EKRCB090715new.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nConjecture &lt;ref&gt; is true if G is a disjoint ...</td>\n",
       "      <td></td>\n",
       "      <td>\\nConjecture &lt;ref&gt; is true if G is a disjoint ...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O B_MATH_TERM O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2573</th>\n",
       "      <td>\\textsf{mnd;\\textsf{mnd</td>\n",
       "      <td>(Borg, Holroyd \\cite{bh})\\label{mnd}\\nFor a mo...</td>\n",
       "      <td>/home/shufan/que_tex/EKRCB090715new.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>(Borg, Holroyd &lt;cit.&gt;)\\nFor a monotonic non-de...</td>\n",
       "      <td></td>\n",
       "      <td>(Borg, Holroyd &lt;cit.&gt;)\\nFor a monotonic non-de...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3193</th>\n",
       "      <td>\\matPoros</td>\n",
       "      <td>[Matching Porosity]\\n\\t\\tLet $S \\subseteq \\Fkt...</td>\n",
       "      <td>/home/shufan/que_tex/pmw2.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>[Matching Porosity]\\n\\t\\tLet S ⊆VG and S be a ...</td>\n",
       "      <td></td>\n",
       "      <td>[Matching Porosity]\\n\\t\\tLet S ⊆VG and S be a ...</td>\n",
       "      <td>O O O O O O O O O O O O O O O B_MATH_TERM O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3682</th>\n",
       "      <td>\\crich{</td>\n",
       "      <td>\\label{def:combrich}%\\label{def:combrich}\\nLet...</td>\n",
       "      <td>/home/shufan/que_tex/largeinsemiringswodynamic...</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nLet  be a commutative semigroup. A subset A ...</td>\n",
       "      <td></td>\n",
       "      <td>\\nLet  be a commutative semigroup. A subset A ...</td>\n",
       "      <td>O O O O O O O O O O O B_MATH_TERM O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3687</th>\n",
       "      <td>\\crich{</td>\n",
       "      <td>\\label{def:combrichuptoe}\\nLet $\\semisplus$ be...</td>\n",
       "      <td>/home/shufan/que_tex/largeinsemiringswodynamic...</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nLet  be a commutative semigroup and  be a su...</td>\n",
       "      <td></td>\n",
       "      <td>\\nLet  be a commutative semigroup and  be a su...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O B_MATH_TER...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5560</th>\n",
       "      <td>\\bpt</td>\n",
       "      <td>\\nA plabic graph $G$ is called \\emph{\\bpt} if ...</td>\n",
       "      <td>/home/shufan/que_tex/HigherSecondaryPolytopes.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nA plabic graph G is called  if all interior ...</td>\n",
       "      <td></td>\n",
       "      <td>\\nA plabic graph G is called B_MATH_TERM if al...</td>\n",
       "      <td>O O O O O O B_MATH_TERM O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6307</th>\n",
       "      <td>\\mbox{$G$-admissible;word-length</td>\n",
       "      <td>\\label{def:g-admissible}\\n\\tLet $\\ell &gt; 1$ and...</td>\n",
       "      <td>/home/shufan/que_tex/synchro-delay-binary-unif...</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\n\\tLet ℓ &gt; 1 and\\n\\t\\n    s_1  s_2   s_3 ⋯  s...</td>\n",
       "      <td></td>\n",
       "      <td>\\n\\tLet ℓ &gt; 1 and\\n\\t\\n    s_1  s_2   s_3 ⋯  s...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6871</th>\n",
       "      <td>\\area</td>\n",
       "      <td>\\label{def:area} If $\\pi$ is a parking functio...</td>\n",
       "      <td>/home/shufan/que_tex/BAMS-shuffle-fin.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>If π is a parking function, then its area is ...</td>\n",
       "      <td></td>\n",
       "      <td>If π is a parking function, then its area is ...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6872</th>\n",
       "      <td>\\dinv</td>\n",
       "      <td>\\label{def:dinv}  Consider a parking function ...</td>\n",
       "      <td>/home/shufan/que_tex/BAMS-shuffle-fin.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>Consider a parking function π, and a pair of...</td>\n",
       "      <td></td>\n",
       "      <td>Consider a parking function π, and a pair of...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6873</th>\n",
       "      <td>\\word</td>\n",
       "      <td>\\label{def:word} If $\\pi$ is a parking functio...</td>\n",
       "      <td>/home/shufan/que_tex/BAMS-shuffle-fin.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>If π is a parking function, then its word is ...</td>\n",
       "      <td></td>\n",
       "      <td>If π is a parking function, then its word is ...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6874</th>\n",
       "      <td>\\ides</td>\n",
       "      <td>\\label{def:ides} If $\\pi$ is a parking functio...</td>\n",
       "      <td>/home/shufan/que_tex/BAMS-shuffle-fin.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>If π is a parking function, then its i-descen...</td>\n",
       "      <td></td>\n",
       "      <td>If π is a parking function, then its i-descen...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6878</th>\n",
       "      <td>\\touch</td>\n",
       "      <td>\\label{def:touch} If $\\pi$ is a parking functi...</td>\n",
       "      <td>/home/shufan/que_tex/BAMS-shuffle-fin.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>If π is a parking function of order n, then n...</td>\n",
       "      <td></td>\n",
       "      <td>If π is a parking function of order n, then n...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7022</th>\n",
       "      <td>\\textsf{GCDS</td>\n",
       "      <td>\\label{cdsgraph}\\nFor each finite graph $\\math...</td>\n",
       "      <td>/home/shufan/que_tex/1411.5429.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nFor each finite graph 𝒢 = (V,  E) and each s...</td>\n",
       "      <td></td>\n",
       "      <td>\\nFor each finite graph 𝒢 = (V,  E) and each s...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7023</th>\n",
       "      <td>\\textsf{N;\\textsf{P</td>\n",
       "      <td>\\label{NPGraphs}\\nLet $(\\mathcal{F},\\textsf{B}...</td>\n",
       "      <td>/home/shufan/que_tex/1411.5429.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet (ℱ,) be a position which, for some posit...</td>\n",
       "      <td></td>\n",
       "      <td>\\nLet (ℱ,) be a position which, for some posit...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7024</th>\n",
       "      <td>\\textsf{CDS;\\textsf{CDS</td>\n",
       "      <td>[\\cite{AHMMSW}, Theorem 4.4]\\label{cdsboundthe...</td>\n",
       "      <td>/home/shufan/que_tex/1411.5429.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>[&lt;cit.&gt;, Theorem 4.4] Let α be a permutation w...</td>\n",
       "      <td></td>\n",
       "      <td>[&lt;cit.&gt;, Theorem 4.4] Let α be a permutation w...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7690</th>\n",
       "      <td>\\exch</td>\n",
       "      <td>\\n  A random infinite graph $H\\in\\cloo$ is \\em...</td>\n",
       "      <td>/home/shufan/que_tex/0712.2749.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\n  A random infinite graph H∈ is  if its\\n  d...</td>\n",
       "      <td></td>\n",
       "      <td>\\n  A random infinite graph H∈ is B_MATH_TERM ...</td>\n",
       "      <td>O O O O O O B_MATH_TERM O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7691</th>\n",
       "      <td>\\exch</td>\n",
       "      <td>\\n  A random infinite bipartite graph $H\\in\\cb...</td>\n",
       "      <td>/home/shufan/que_tex/0712.2749.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\n  A random infinite bipartite graph H∈ is  i...</td>\n",
       "      <td></td>\n",
       "      <td>\\n  A random infinite bipartite graph H∈ is B_...</td>\n",
       "      <td>O O O O O O O B_MATH_TERM O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7994</th>\n",
       "      <td>\\textsf{std</td>\n",
       "      <td>\\n\\label{injection}\\nThe map $\\emph{\\textsf{st...</td>\n",
       "      <td>/home/shufan/que_tex/1908.11455.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n\\nThe map :  EG(λ,w)→ SYT(λ) is an injection.\\n</td>\n",
       "      <td></td>\n",
       "      <td>\\n\\nThe map B_MATH_TERM:  EG(λ,w)→ SYT(λ) is a...</td>\n",
       "      <td>O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8024</th>\n",
       "      <td>\\invf</td>\n",
       "      <td>\\nGiven a {\\fds} ${\\cal U}$, a factor of $U^2$...</td>\n",
       "      <td>/home/shufan/que_tex/da3474.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nGiven a  U, a factor of U^2 of length \\n2|u_...</td>\n",
       "      <td></td>\n",
       "      <td>\\nGiven a  U, a factor of U^2 of length \\n2|u_...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O B_MATH_TERM O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8442</th>\n",
       "      <td>\\textup{(</td>\n",
       "      <td>[Nilsequences]\\nA \\emph{\\textup{(}polynomial\\t...</td>\n",
       "      <td>/home/shufan/que_tex/1505.06479.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>[Nilsequences]\\nA polynomial nilsequence of de...</td>\n",
       "      <td></td>\n",
       "      <td>[Nilsequences]\\nA B_MATH_TERMpolynomial nilseq...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8738</th>\n",
       "      <td>\\PM</td>\n",
       "      <td>\\label{def:murder}\\nThe \\emph{\\PM} of rank $n$...</td>\n",
       "      <td>/home/shufan/que_tex/1807.11297.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nThe  of rank n, M_n∈ℰ, is recursively define...</td>\n",
       "      <td></td>\n",
       "      <td>\\nThe B_MATH_TERM of rank n, M_n∈ℰ, is recursi...</td>\n",
       "      <td>O B_MATH_TERM O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9175</th>\n",
       "      <td>{\\red</td>\n",
       "      <td>\\label{def:red}\\nWe say that  $\\tau\\in\\Faces$ ...</td>\n",
       "      <td>/home/shufan/que_tex/article_PCC_graph_arxiv_p...</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nWe say that  τ∈ with τ=3 is a triangle if \\n...</td>\n",
       "      <td></td>\n",
       "      <td>\\nWe say that  τ∈ with τ=3 is a B_MATH_TERMtri...</td>\n",
       "      <td>O O O O O O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9234</th>\n",
       "      <td>$\\tilde{\\jmath</td>\n",
       "      <td>\\nLet $J$ be a graph and $S$ a set. The \\emph{...</td>\n",
       "      <td>/home/shufan/que_tex/arxiv3.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nLet J be a graph and S a set. The –polynomia...</td>\n",
       "      <td></td>\n",
       "      <td>\\nLet J be a graph and S a set. The B_MATH_TER...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9867</th>\n",
       "      <td>\\ocrossing{</td>\n",
       "      <td>Let $X$ and $Y$ be convex subsets of the Eucl...</td>\n",
       "      <td>/home/shufan/que_tex/czg-circles-and-crossing-...</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>Let X and Y be convex subsets of the Euclidea...</td>\n",
       "      <td></td>\n",
       "      <td>Let X and Y be convex subsets of the Euclidea...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O B_MATH_TER...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9926</th>\n",
       "      <td>\\NIM</td>\n",
       "      <td>\\label{thm-exact}\\n \\tLet $(H_1,\\ldots,H_k)$ b...</td>\n",
       "      <td>/home/shufan/que_tex/NIM-3rd-revision-0710.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n \\tLet (H_1,…,H_k) be a nice sequence of non...</td>\n",
       "      <td></td>\n",
       "      <td>\\n \\tLet (H_1,…,H_k) be a nice sequence of non...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10430</th>\n",
       "      <td>\\reg</td>\n",
       "      <td>\\label{AppRegConj}\\nFor every $\\varepsilon&gt;0$ ...</td>\n",
       "      <td>/home/shufan/que_tex/1212.4667.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nFor every ε&gt;0 and a sufficiently large integ...</td>\n",
       "      <td></td>\n",
       "      <td>\\nFor every ε&gt;0 and a sufficiently large integ...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10613</th>\n",
       "      <td>\\hspace{0.3 cm;\\hspace{0.3 cm</td>\n",
       "      <td>[Lin]\\n\\label{thm:lin} If $T$ and $T'$ are two...</td>\n",
       "      <td>/home/shufan/que_tex/survey-before_submission-...</td>\n",
       "      <td>theorem + \\textit{}</td>\n",
       "      <td>[Lin]\\n If T and T' are two trees on the same ...</td>\n",
       "      <td></td>\n",
       "      <td>[Lin]\\n If T and T' are two trees on the same ...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O B_...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11493</th>\n",
       "      <td>\\Ccomp</td>\n",
       "      <td>\\nWe call an \\Ocomp\\ of $G$ a \\emph{\\Ccomp } o...</td>\n",
       "      <td>/home/shufan/que_tex/EndsTanglesCrit.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nWe call an  of G a  of G if it is induced by...</td>\n",
       "      <td></td>\n",
       "      <td>\\nWe call an  of G a B_MATH_TERM of G if it is...</td>\n",
       "      <td>O O O O O O B_MATH_TERM O O O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11789</th>\n",
       "      <td>\\StoneCech</td>\n",
       "      <td>\\label{definition-stone-cech}\\nThe \\define{\\St...</td>\n",
       "      <td>/home/shufan/que_tex/Diplomarbeit.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>\\nThe  β X of a topological space X is a compa...</td>\n",
       "      <td></td>\n",
       "      <td>\\nThe B_MATH_TERM β X of a topological space X...</td>\n",
       "      <td>O B_MATH_TERM O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11814</th>\n",
       "      <td>\\aprich</td>\n",
       "      <td>[Progression-rich ultrafilters]\\n\\label{defini...</td>\n",
       "      <td>/home/shufan/que_tex/Diplomarbeit.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>[Progression-rich ultrafilters]\\n\\nAn ultrafil...</td>\n",
       "      <td></td>\n",
       "      <td>[Progression-rich ultrafilters]\\n\\nAn ultrafil...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12613</th>\n",
       "      <td>\\Wfsf</td>\n",
       "      <td>\\label{def-wfsf}\\n  Let~$G=(V,E)$ be a graph w...</td>\n",
       "      <td>/home/shufan/que_tex/planar-nocom.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>\\n  Let G=(V,E) be a graph with a fixed plane ...</td>\n",
       "      <td></td>\n",
       "      <td>\\n  Let G=(V,E) be a graph with a fixed plane ...</td>\n",
       "      <td>O O O O O O O O O O O O O O O B_MATH_TERM O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12790</th>\n",
       "      <td>$\\check{\\mbox{C;The local cohomology of $M$ wi...</td>\n",
       "      <td>\\label{Def LC}\\nLet $I\\subseteq R$ be a  ideal...</td>\n",
       "      <td>/home/shufan/que_tex/GraphConnectivityBinomial...</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nLet I⊆ R be a  ideal  generated by polynomia...</td>\n",
       "      <td></td>\n",
       "      <td>\\nLet I⊆ R be a  ideal  generated by polynomia...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12942</th>\n",
       "      <td>\\eeq</td>\n",
       "      <td>\\label{Dee}\\n  Two graphons $(W_1,S_1)$ and $(...</td>\n",
       "      <td>/home/shufan/que_tex/1608.01833.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\n  Two graphons (W_1,S_1) and (W_2,S_2) are \\...</td>\n",
       "      <td></td>\n",
       "      <td>\\n  Two graphons (W_1,S_1) and (W_2,S_2) are B...</td>\n",
       "      <td>O O O O O O B_MATH_TERM O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12963</th>\n",
       "      <td>\\sseq</td>\n",
       "      <td>\\nThe sequence $\\inr$ from \\eqref{eqsseqpseq} ...</td>\n",
       "      <td>/home/shufan/que_tex/czg-makay-swinglem-2016ju...</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nThe sequence  from (&lt;ref&gt;) is an  if for eac...</td>\n",
       "      <td></td>\n",
       "      <td>\\nThe sequence  from (&lt;ref&gt;) is an B_MATH_TERM...</td>\n",
       "      <td>O O O O O O B_MATH_TERM O O O O O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13090</th>\n",
       "      <td>\\splitf{</td>\n",
       "      <td>\\nWe say that a Boolean function $f = f(x_1, \\...</td>\n",
       "      <td>/home/shufan/que_tex/1706.01747.tex</td>\n",
       "      <td>definition + \\textit{}</td>\n",
       "      <td>\\nWe say that a Boolean function f = f(x_1, …,...</td>\n",
       "      <td></td>\n",
       "      <td>\\nWe say that a Boolean function f = f(x_1, …,...</td>\n",
       "      <td>O O O O O O O O O O O O B_MATH_TERM O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14223</th>\n",
       "      <td>\\slw</td>\n",
       "      <td>On appellera un \\slw, un chemin $\\Gamma$ de cl...</td>\n",
       "      <td>/home/shufan/que_tex/enumeration_construction_...</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>On appellera un , un chemin Γ de classe 𝒞^1 de...</td>\n",
       "      <td></td>\n",
       "      <td>On appellera un B_MATH_TERM, un chemin Γ de cl...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14225</th>\n",
       "      <td>\\slw</td>\n",
       "      <td>We will call a \\slw, a path $\\Gamma$ of class ...</td>\n",
       "      <td>/home/shufan/que_tex/enumeration_construction_...</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>We will call a , a path Γ of class 𝒞^1 in ^2, ...</td>\n",
       "      <td></td>\n",
       "      <td>We will call a B_MATH_TERM, a path Γ of class ...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15355</th>\n",
       "      <td>\\btree</td>\n",
       "      <td>A \\emph{\\btree} is a rooted\\nplane tree label...</td>\n",
       "      <td>/home/shufan/que_tex/fixed-points-h-final.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>A  is a rooted\\nplane tree labeled with posit...</td>\n",
       "      <td></td>\n",
       "      <td>A B_MATH_TERM is a rooted\\nplane tree labeled...</td>\n",
       "      <td>O B_MATH_TERM O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17155</th>\n",
       "      <td>\\wcr</td>\n",
       "      <td>We will call a flow $f$ in a network $\\Delta=(...</td>\n",
       "      <td>/home/shufan/que_tex/MFMC_final.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>We will call a flow f in a network Δ=(D,c,s,t)...</td>\n",
       "      <td></td>\n",
       "      <td>We will call a flow f in a network Δ=(D,c,s,t)...</td>\n",
       "      <td>O O O O O O O O O O B_MATH_TERM O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17156</th>\n",
       "      <td>\\scr</td>\n",
       "      <td>\\nWe will call a flow $f$ in a network $\\Delta...</td>\n",
       "      <td>/home/shufan/que_tex/MFMC_final.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nWe will call a flow f in a network Δ=(D,c,s,...</td>\n",
       "      <td></td>\n",
       "      <td>\\nWe will call a flow f in a network Δ=(D,c,s,...</td>\n",
       "      <td>O O O O O O O O O O B_MATH_TERM O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17657</th>\n",
       "      <td>\\medskip</td>\n",
       "      <td>\\n\\tLet $(Q,N)$ be an $\\ell$-reflexive pair an...</td>\n",
       "      <td>/home/shufan/que_tex/Twelveptthm.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\n\\tLet (Q,N) be an ℓ-reflexive pair and M:= H...</td>\n",
       "      <td></td>\n",
       "      <td>\\n\\tLet (Q,N) be an ℓ-reflexive pair and M:= H...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                    term  \\\n",
       "129                                             \\Csimple   \n",
       "1033                                         \\Cyclewidth   \n",
       "1045                                           \\cycPoros   \n",
       "1047                                           \\matPoros   \n",
       "1598                                                \\edg   \n",
       "1599                                                \\edg   \n",
       "2066                                             \\robust   \n",
       "2127                                               $\\EK$   \n",
       "2128                                              $\\LEK$   \n",
       "2129                                          $\\QOPstar$   \n",
       "2130                                              $\\QOP$   \n",
       "2571                                         \\textsf{mnd   \n",
       "2573                             \\textsf{mnd;\\textsf{mnd   \n",
       "3193                                           \\matPoros   \n",
       "3682                                             \\crich{   \n",
       "3687                                             \\crich{   \n",
       "5560                                                \\bpt   \n",
       "6307                    \\mbox{$G$-admissible;word-length   \n",
       "6871                                               \\area   \n",
       "6872                                               \\dinv   \n",
       "6873                                               \\word   \n",
       "6874                                               \\ides   \n",
       "6878                                              \\touch   \n",
       "7022                                        \\textsf{GCDS   \n",
       "7023                                 \\textsf{N;\\textsf{P   \n",
       "7024                             \\textsf{CDS;\\textsf{CDS   \n",
       "7690                                               \\exch   \n",
       "7691                                               \\exch   \n",
       "7994                                         \\textsf{std   \n",
       "8024                                               \\invf   \n",
       "8442                                           \\textup{(   \n",
       "8738                                                 \\PM   \n",
       "9175                                               {\\red   \n",
       "9234                                      $\\tilde{\\jmath   \n",
       "9867                                         \\ocrossing{   \n",
       "9926                                                \\NIM   \n",
       "10430                                               \\reg   \n",
       "10613                      \\hspace{0.3 cm;\\hspace{0.3 cm   \n",
       "11493                                            \\Ccomp    \n",
       "11789                                         \\StoneCech   \n",
       "11814                                            \\aprich   \n",
       "12613                                              \\Wfsf   \n",
       "12790  $\\check{\\mbox{C;The local cohomology of $M$ wi...   \n",
       "12942                                               \\eeq   \n",
       "12963                                              \\sseq   \n",
       "13090                                           \\splitf{   \n",
       "14223                                               \\slw   \n",
       "14225                                               \\slw   \n",
       "15355                                             \\btree   \n",
       "17155                                               \\wcr   \n",
       "17156                                               \\scr   \n",
       "17657                                           \\medskip   \n",
       "\n",
       "                                                     def  \\\n",
       "129    Let $P$ be a polyhedron. We say $P$ is \\Csimpl...   \n",
       "1033   Let $D$ be a \\digraph.\\n\\t\\tA cycle decomposit...   \n",
       "1045   [\\Cyclewidth]\\n\\t\\tLet $D$ be a \\digraph.\\n\\t\\...   \n",
       "1047   [matching-porosity]\\n\\t\\tLet $G$ be a matching...   \n",
       "1598   [non-boundary edge classes]\\label{def:non-boun...   \n",
       "1599   [forward extension]\\label{def:forward-ext}\\nLe...   \n",
       "2066   Given two sets $A \\subseteq L$ and $B \\subsete...   \n",
       "2127   Let $\\K$ be a class of structures in $L_I := \\...   \n",
       "2128   Let $L_I := \\{R_i : i \\in I\\}$ and $L_J := \\{R...   \n",
       "2129   Let $(\\K,\\K^*)$ be an excellent pair. We say t...   \n",
       "2130   Let $(\\K,\\K^*)$ be an excellent pair. We say t...   \n",
       "2571   \\label{bhth}\\nConjecture \\ref{minmax} is true ...   \n",
       "2573   (Borg, Holroyd \\cite{bh})\\label{mnd}\\nFor a mo...   \n",
       "3193   [Matching Porosity]\\n\\t\\tLet $S \\subseteq \\Fkt...   \n",
       "3682   \\label{def:combrich}%\\label{def:combrich}\\nLet...   \n",
       "3687   \\label{def:combrichuptoe}\\nLet $\\semisplus$ be...   \n",
       "5560   \\nA plabic graph $G$ is called \\emph{\\bpt} if ...   \n",
       "6307   \\label{def:g-admissible}\\n\\tLet $\\ell > 1$ and...   \n",
       "6871   \\label{def:area} If $\\pi$ is a parking functio...   \n",
       "6872   \\label{def:dinv}  Consider a parking function ...   \n",
       "6873   \\label{def:word} If $\\pi$ is a parking functio...   \n",
       "6874   \\label{def:ides} If $\\pi$ is a parking functio...   \n",
       "6878   \\label{def:touch} If $\\pi$ is a parking functi...   \n",
       "7022   \\label{cdsgraph}\\nFor each finite graph $\\math...   \n",
       "7023   \\label{NPGraphs}\\nLet $(\\mathcal{F},\\textsf{B}...   \n",
       "7024   [\\cite{AHMMSW}, Theorem 4.4]\\label{cdsboundthe...   \n",
       "7690   \\n  A random infinite graph $H\\in\\cloo$ is \\em...   \n",
       "7691   \\n  A random infinite bipartite graph $H\\in\\cb...   \n",
       "7994   \\n\\label{injection}\\nThe map $\\emph{\\textsf{st...   \n",
       "8024   \\nGiven a {\\fds} ${\\cal U}$, a factor of $U^2$...   \n",
       "8442   [Nilsequences]\\nA \\emph{\\textup{(}polynomial\\t...   \n",
       "8738   \\label{def:murder}\\nThe \\emph{\\PM} of rank $n$...   \n",
       "9175   \\label{def:red}\\nWe say that  $\\tau\\in\\Faces$ ...   \n",
       "9234   \\nLet $J$ be a graph and $S$ a set. The \\emph{...   \n",
       "9867    Let $X$ and $Y$ be convex subsets of the Eucl...   \n",
       "9926   \\label{thm-exact}\\n \\tLet $(H_1,\\ldots,H_k)$ b...   \n",
       "10430  \\label{AppRegConj}\\nFor every $\\varepsilon>0$ ...   \n",
       "10613  [Lin]\\n\\label{thm:lin} If $T$ and $T'$ are two...   \n",
       "11493  \\nWe call an \\Ocomp\\ of $G$ a \\emph{\\Ccomp } o...   \n",
       "11789  \\label{definition-stone-cech}\\nThe \\define{\\St...   \n",
       "11814  [Progression-rich ultrafilters]\\n\\label{defini...   \n",
       "12613  \\label{def-wfsf}\\n  Let~$G=(V,E)$ be a graph w...   \n",
       "12790  \\label{Def LC}\\nLet $I\\subseteq R$ be a  ideal...   \n",
       "12942  \\label{Dee}\\n  Two graphons $(W_1,S_1)$ and $(...   \n",
       "12963  \\nThe sequence $\\inr$ from \\eqref{eqsseqpseq} ...   \n",
       "13090  \\nWe say that a Boolean function $f = f(x_1, \\...   \n",
       "14223  On appellera un \\slw, un chemin $\\Gamma$ de cl...   \n",
       "14225  We will call a \\slw, a path $\\Gamma$ of class ...   \n",
       "15355   A \\emph{\\btree} is a rooted\\nplane tree label...   \n",
       "17155  We will call a flow $f$ in a network $\\Delta=(...   \n",
       "17156  \\nWe will call a flow $f$ in a network $\\Delta...   \n",
       "17657  \\n\\tLet $(Q,N)$ be an $\\ell$-reflexive pair an...   \n",
       "\n",
       "                                               file_name  \\\n",
       "129                  /home/shufan/que_tex/oncircuits.tex   \n",
       "1033                    /home/shufan/que_tex/bipgrid.tex   \n",
       "1045                    /home/shufan/que_tex/bipgrid.tex   \n",
       "1047                    /home/shufan/que_tex/bipgrid.tex   \n",
       "1598                 /home/shufan/que_tex/trilongest.tex   \n",
       "1599                 /home/shufan/que_tex/trilongest.tex   \n",
       "2066                 /home/shufan/que_tex/eccc-arxiv.tex   \n",
       "2127   /home/shufan/que_tex/Sokic_Pawliuk_amenable_au...   \n",
       "2128   /home/shufan/que_tex/Sokic_Pawliuk_amenable_au...   \n",
       "2129   /home/shufan/que_tex/Sokic_Pawliuk_amenable_au...   \n",
       "2130   /home/shufan/que_tex/Sokic_Pawliuk_amenable_au...   \n",
       "2571             /home/shufan/que_tex/EKRCB090715new.tex   \n",
       "2573             /home/shufan/que_tex/EKRCB090715new.tex   \n",
       "3193                       /home/shufan/que_tex/pmw2.tex   \n",
       "3682   /home/shufan/que_tex/largeinsemiringswodynamic...   \n",
       "3687   /home/shufan/que_tex/largeinsemiringswodynamic...   \n",
       "5560   /home/shufan/que_tex/HigherSecondaryPolytopes.tex   \n",
       "6307   /home/shufan/que_tex/synchro-delay-binary-unif...   \n",
       "6871           /home/shufan/que_tex/BAMS-shuffle-fin.tex   \n",
       "6872           /home/shufan/que_tex/BAMS-shuffle-fin.tex   \n",
       "6873           /home/shufan/que_tex/BAMS-shuffle-fin.tex   \n",
       "6874           /home/shufan/que_tex/BAMS-shuffle-fin.tex   \n",
       "6878           /home/shufan/que_tex/BAMS-shuffle-fin.tex   \n",
       "7022                  /home/shufan/que_tex/1411.5429.tex   \n",
       "7023                  /home/shufan/que_tex/1411.5429.tex   \n",
       "7024                  /home/shufan/que_tex/1411.5429.tex   \n",
       "7690                  /home/shufan/que_tex/0712.2749.tex   \n",
       "7691                  /home/shufan/que_tex/0712.2749.tex   \n",
       "7994                 /home/shufan/que_tex/1908.11455.tex   \n",
       "8024                     /home/shufan/que_tex/da3474.tex   \n",
       "8442                 /home/shufan/que_tex/1505.06479.tex   \n",
       "8738                 /home/shufan/que_tex/1807.11297.tex   \n",
       "9175   /home/shufan/que_tex/article_PCC_graph_arxiv_p...   \n",
       "9234                     /home/shufan/que_tex/arxiv3.tex   \n",
       "9867   /home/shufan/que_tex/czg-circles-and-crossing-...   \n",
       "9926      /home/shufan/que_tex/NIM-3rd-revision-0710.tex   \n",
       "10430                 /home/shufan/que_tex/1212.4667.tex   \n",
       "10613  /home/shufan/que_tex/survey-before_submission-...   \n",
       "11493           /home/shufan/que_tex/EndsTanglesCrit.tex   \n",
       "11789              /home/shufan/que_tex/Diplomarbeit.tex   \n",
       "11814              /home/shufan/que_tex/Diplomarbeit.tex   \n",
       "12613              /home/shufan/que_tex/planar-nocom.tex   \n",
       "12790  /home/shufan/que_tex/GraphConnectivityBinomial...   \n",
       "12942                /home/shufan/que_tex/1608.01833.tex   \n",
       "12963  /home/shufan/que_tex/czg-makay-swinglem-2016ju...   \n",
       "13090                /home/shufan/que_tex/1706.01747.tex   \n",
       "14223  /home/shufan/que_tex/enumeration_construction_...   \n",
       "14225  /home/shufan/que_tex/enumeration_construction_...   \n",
       "15355      /home/shufan/que_tex/fixed-points-h-final.tex   \n",
       "17155                /home/shufan/que_tex/MFMC_final.tex   \n",
       "17156                /home/shufan/que_tex/MFMC_final.tex   \n",
       "17657               /home/shufan/que_tex/Twelveptthm.tex   \n",
       "\n",
       "              extraction_rule  \\\n",
       "129              definition[]   \n",
       "1033             definition[]   \n",
       "1045     definition + \\emph{}   \n",
       "1047     definition + \\emph{}   \n",
       "1598     definition + \\emph{}   \n",
       "1599     definition + \\emph{}   \n",
       "2066             definition[]   \n",
       "2127             definition[]   \n",
       "2128             definition[]   \n",
       "2129             definition[]   \n",
       "2130             definition[]   \n",
       "2571        theorem + \\emph{}   \n",
       "2573     definition + \\emph{}   \n",
       "3193     definition + \\emph{}   \n",
       "3682     definition + \\emph{}   \n",
       "3687     definition + \\emph{}   \n",
       "5560     definition + \\emph{}   \n",
       "6307     definition + \\emph{}   \n",
       "6871             definition[]   \n",
       "6872             definition[]   \n",
       "6873             definition[]   \n",
       "6874             definition[]   \n",
       "6878             definition[]   \n",
       "7022        theorem + \\emph{}   \n",
       "7023        theorem + \\emph{}   \n",
       "7024        theorem + \\emph{}   \n",
       "7690     definition + \\emph{}   \n",
       "7691     definition + \\emph{}   \n",
       "7994        theorem + \\emph{}   \n",
       "8024     definition + \\emph{}   \n",
       "8442     definition + \\emph{}   \n",
       "8738     definition + \\emph{}   \n",
       "9175     definition + \\emph{}   \n",
       "9234     definition + \\emph{}   \n",
       "9867     definition + \\emph{}   \n",
       "9926        theorem + \\emph{}   \n",
       "10430       theorem + \\emph{}   \n",
       "10613     theorem + \\textit{}   \n",
       "11493    definition + \\emph{}   \n",
       "11789            definition[]   \n",
       "11814    definition + \\emph{}   \n",
       "12613            definition[]   \n",
       "12790    definition + \\emph{}   \n",
       "12942    definition + \\emph{}   \n",
       "12963    definition + \\emph{}   \n",
       "13090  definition + \\textit{}   \n",
       "14223            definition[]   \n",
       "14225            definition[]   \n",
       "15355    definition + \\emph{}   \n",
       "17155    definition + \\emph{}   \n",
       "17156    definition + \\emph{}   \n",
       "17657    definition + \\emph{}   \n",
       "\n",
       "                                          plain_text_def plain_text_term  \\\n",
       "129    Let P be a polyhedron. We say P is  if all cir...                   \n",
       "1033   Let D be a .\\n\\t\\tA cycle decomposition of D i...                   \n",
       "1045   []\\n\\t\\tLet D be a .\\n\\t\\tA cycle decompositio...                   \n",
       "1047   [matching-porosity]\\n\\t\\tLet G be a matching c...                   \n",
       "1598   [non-boundary edge classes] Let _π be an M-bou...                   \n",
       "1599   [forward extension]\\nLet _π be an M-bounded tr...                   \n",
       "2066   Given two sets A ⊆ L and B ⊆ R, we say that th...                   \n",
       "2127   Let  be a class of structures in L_I := {R_i :...                   \n",
       "2128   Let L_I := {R_i : i ∈ I} and L_J := {R_j : j ∈...                   \n",
       "2129   Let (,^*) be an excellent pair. We say that ^*...                   \n",
       "2130   Let (,^*) be an excellent pair. We say that ^*...                   \n",
       "2571   \\nConjecture <ref> is true if G is a disjoint ...                   \n",
       "2573   (Borg, Holroyd <cit.>)\\nFor a monotonic non-de...                   \n",
       "3193   [Matching Porosity]\\n\\t\\tLet S ⊆VG and S be a ...                   \n",
       "3682   \\nLet  be a commutative semigroup. A subset A ...                   \n",
       "3687   \\nLet  be a commutative semigroup and  be a su...                   \n",
       "5560   \\nA plabic graph G is called  if all interior ...                   \n",
       "6307   \\n\\tLet ℓ > 1 and\\n\\t\\n    s_1  s_2   s_3 ⋯  s...                   \n",
       "6871    If π is a parking function, then its area is ...                   \n",
       "6872     Consider a parking function π, and a pair of...                   \n",
       "6873    If π is a parking function, then its word is ...                   \n",
       "6874    If π is a parking function, then its i-descen...                   \n",
       "6878    If π is a parking function of order n, then n...                   \n",
       "7022   \\nFor each finite graph 𝒢 = (V,  E) and each s...                   \n",
       "7023   \\nLet (ℱ,) be a position which, for some posit...                   \n",
       "7024   [<cit.>, Theorem 4.4] Let α be a permutation w...                   \n",
       "7690   \\n  A random infinite graph H∈ is  if its\\n  d...                   \n",
       "7691   \\n  A random infinite bipartite graph H∈ is  i...                   \n",
       "7994   \\n\\nThe map :  EG(λ,w)→ SYT(λ) is an injection.\\n                   \n",
       "8024   \\nGiven a  U, a factor of U^2 of length \\n2|u_...                   \n",
       "8442   [Nilsequences]\\nA polynomial nilsequence of de...                   \n",
       "8738   \\nThe  of rank n, M_n∈ℰ, is recursively define...                   \n",
       "9175   \\nWe say that  τ∈ with τ=3 is a triangle if \\n...                   \n",
       "9234   \\nLet J be a graph and S a set. The –polynomia...                   \n",
       "9867    Let X and Y be convex subsets of the Euclidea...                   \n",
       "9926   \\n \\tLet (H_1,…,H_k) be a nice sequence of non...                   \n",
       "10430  \\nFor every ε>0 and a sufficiently large integ...                   \n",
       "10613  [Lin]\\n If T and T' are two trees on the same ...                   \n",
       "11493  \\nWe call an  of G a  of G if it is induced by...                   \n",
       "11789  \\nThe  β X of a topological space X is a compa...                   \n",
       "11814  [Progression-rich ultrafilters]\\n\\nAn ultrafil...                   \n",
       "12613  \\n  Let G=(V,E) be a graph with a fixed plane ...                   \n",
       "12790  \\nLet I⊆ R be a  ideal  generated by polynomia...                   \n",
       "12942  \\n  Two graphons (W_1,S_1) and (W_2,S_2) are \\...                   \n",
       "12963  \\nThe sequence  from (<ref>) is an  if for eac...                   \n",
       "13090  \\nWe say that a Boolean function f = f(x_1, …,...                   \n",
       "14223  On appellera un , un chemin Γ de classe 𝒞^1 de...                   \n",
       "14225  We will call a , a path Γ of class 𝒞^1 in ^2, ...                   \n",
       "15355   A  is a rooted\\nplane tree labeled with posit...                   \n",
       "17155  We will call a flow f in a network Δ=(D,c,s,t)...                   \n",
       "17156  \\nWe will call a flow f in a network Δ=(D,c,s,...                   \n",
       "17657  \\n\\tLet (Q,N) be an ℓ-reflexive pair and M:= H...                   \n",
       "\n",
       "                                   masked_plain_text_def  \\\n",
       "129    Let P be a polyhedron. We say P is B_MATH_TERM...   \n",
       "1033   Let D be a .\\n\\t\\tA cycle decomposition of D i...   \n",
       "1045   []\\n\\t\\tLet D be a .\\n\\t\\tA cycle decompositio...   \n",
       "1047   [matching-porosity]\\n\\t\\tLet G be a matching c...   \n",
       "1598   [non-boundary edge classes] Let _π be an M-bou...   \n",
       "1599   [forward extension]\\nLet _π be an M-bounded tr...   \n",
       "2066   Given two sets A ⊆ L and B ⊆ R, we say that th...   \n",
       "2127   Let  be a class of structures in L_I := {R_i :...   \n",
       "2128   Let L_I := {R_i : i ∈ I} and L_J := {R_j : j ∈...   \n",
       "2129   Let (,^*) be an excellent pair. We say that ^*...   \n",
       "2130   Let (,^*) be an excellent pair. We say that ^*...   \n",
       "2571   \\nConjecture <ref> is true if G is a disjoint ...   \n",
       "2573   (Borg, Holroyd <cit.>)\\nFor a monotonic non-de...   \n",
       "3193   [Matching Porosity]\\n\\t\\tLet S ⊆VG and S be a ...   \n",
       "3682   \\nLet  be a commutative semigroup. A subset A ...   \n",
       "3687   \\nLet  be a commutative semigroup and  be a su...   \n",
       "5560   \\nA plabic graph G is called B_MATH_TERM if al...   \n",
       "6307   \\n\\tLet ℓ > 1 and\\n\\t\\n    s_1  s_2   s_3 ⋯  s...   \n",
       "6871    If π is a parking function, then its area is ...   \n",
       "6872     Consider a parking function π, and a pair of...   \n",
       "6873    If π is a parking function, then its word is ...   \n",
       "6874    If π is a parking function, then its i-descen...   \n",
       "6878    If π is a parking function of order n, then n...   \n",
       "7022   \\nFor each finite graph 𝒢 = (V,  E) and each s...   \n",
       "7023   \\nLet (ℱ,) be a position which, for some posit...   \n",
       "7024   [<cit.>, Theorem 4.4] Let α be a permutation w...   \n",
       "7690   \\n  A random infinite graph H∈ is B_MATH_TERM ...   \n",
       "7691   \\n  A random infinite bipartite graph H∈ is B_...   \n",
       "7994   \\n\\nThe map B_MATH_TERM:  EG(λ,w)→ SYT(λ) is a...   \n",
       "8024   \\nGiven a  U, a factor of U^2 of length \\n2|u_...   \n",
       "8442   [Nilsequences]\\nA B_MATH_TERMpolynomial nilseq...   \n",
       "8738   \\nThe B_MATH_TERM of rank n, M_n∈ℰ, is recursi...   \n",
       "9175   \\nWe say that  τ∈ with τ=3 is a B_MATH_TERMtri...   \n",
       "9234   \\nLet J be a graph and S a set. The B_MATH_TER...   \n",
       "9867    Let X and Y be convex subsets of the Euclidea...   \n",
       "9926   \\n \\tLet (H_1,…,H_k) be a nice sequence of non...   \n",
       "10430  \\nFor every ε>0 and a sufficiently large integ...   \n",
       "10613  [Lin]\\n If T and T' are two trees on the same ...   \n",
       "11493  \\nWe call an  of G a B_MATH_TERM of G if it is...   \n",
       "11789  \\nThe B_MATH_TERM β X of a topological space X...   \n",
       "11814  [Progression-rich ultrafilters]\\n\\nAn ultrafil...   \n",
       "12613  \\n  Let G=(V,E) be a graph with a fixed plane ...   \n",
       "12790  \\nLet I⊆ R be a  ideal  generated by polynomia...   \n",
       "12942  \\n  Two graphons (W_1,S_1) and (W_2,S_2) are B...   \n",
       "12963  \\nThe sequence  from (<ref>) is an B_MATH_TERM...   \n",
       "13090  \\nWe say that a Boolean function f = f(x_1, …,...   \n",
       "14223  On appellera un B_MATH_TERM, un chemin Γ de cl...   \n",
       "14225  We will call a B_MATH_TERM, a path Γ of class ...   \n",
       "15355   A B_MATH_TERM is a rooted\\nplane tree labeled...   \n",
       "17155  We will call a flow f in a network Δ=(D,c,s,t)...   \n",
       "17156  \\nWe will call a flow f in a network Δ=(D,c,s,...   \n",
       "17657  \\n\\tLet (Q,N) be an ℓ-reflexive pair and M:= H...   \n",
       "\n",
       "                                             labeled_def  \n",
       "129    O O O O O O O O O B_MATH_TERM O O O O O O O O ...  \n",
       "1033   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "1045   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "1047     O O O O O O O O O O O O O B_MATH_TERM O O O O O  \n",
       "1598   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "1599   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "2066   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "2127   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "2128   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "2129   O O O O O O O O O O O O B_MATH_TERM O O O O O ...  \n",
       "2130   O O O O O O O O O O O O B_MATH_TERM O O O O O ...  \n",
       "2571   O O O O O O O O O O O O O O O O B_MATH_TERM O ...  \n",
       "2573   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "3193   O O O O O O O O O O O O O O O B_MATH_TERM O O ...  \n",
       "3682   O O O O O O O O O O O B_MATH_TERM O O O O O O ...  \n",
       "3687   O O O O O O O O O O O O O O O O O O B_MATH_TER...  \n",
       "5560   O O O O O O B_MATH_TERM O O O O O O O O O O O ...  \n",
       "6307   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "6871   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "6872   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "6873   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "6874                   O O O O O O O O O O O O O O O O O  \n",
       "6878   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "7022   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "7023   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "7024   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "7690   O O O O O O B_MATH_TERM O O O O O O O O O O O ...  \n",
       "7691   O O O O O O O B_MATH_TERM O O O O O O O O O O ...  \n",
       "7994                                     O O O O O O O O  \n",
       "8024   O O O O O O O O O O O O O O O O B_MATH_TERM O ...  \n",
       "8442   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "8738   O B_MATH_TERM O O O O O O O O O O O O O O O O ...  \n",
       "9175                           O O O O O O O O O O O O O  \n",
       "9234           O O O O O O O O O O O O O O O O O O O O O  \n",
       "9867   O O O O O O O O O O O O O O O O O O B_MATH_TER...  \n",
       "9926   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "10430  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "10613  O O O O O O O O O O O O O O O O O O O O O O B_...  \n",
       "11493        O O O O O O B_MATH_TERM O O O O O O O O O O  \n",
       "11789  O B_MATH_TERM O O O O O O O O O O O O O O O O ...  \n",
       "11814  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "12613  O O O O O O O O O O O O O O O B_MATH_TERM O O ...  \n",
       "12790  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "12942  O O O O O O B_MATH_TERM O O O O O O O O O O O ...  \n",
       "12963    O O O O O O B_MATH_TERM O O O O O O O O O O O O  \n",
       "13090  O O O O O O O O O O O O B_MATH_TERM O O O O O ...  \n",
       "14223  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "14225  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "15355  O B_MATH_TERM O O O O O O O O O O O O O O O O ...  \n",
       "17155  O O O O O O O O O O B_MATH_TERM O O O O O O O ...  \n",
       "17156  O O O O O O O O O O B_MATH_TERM O O O O O O O ...  \n",
       "17657  O O O O O O O O O O O O O O O O O O O O O O O ...  "
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "is_empty_or_only_whitespaces = df_clean['plain_text_term'].str.isspace() | df_clean['plain_text_term'].str.len() == 0\n",
    "df_clean[is_empty_or_only_whitespaces]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "596a8d0d-3805-4d3a-9591-55aa40497841",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>term</th>\n",
       "      <th>def</th>\n",
       "      <th>file_name</th>\n",
       "      <th>extraction_rule</th>\n",
       "      <th>plain_text_def</th>\n",
       "      <th>plain_text_term</th>\n",
       "      <th>masked_plain_text_def</th>\n",
       "      <th>labeled_def</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>admissible $G$-cover</td>\n",
       "      <td>\\label{def_admissibleGcover}\\nLet $G$ be a fin...</td>\n",
       "      <td>/home/shufan/que_tex/abelian_tropical_covers.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nLet G be a finite group and let X→ S be a fa...</td>\n",
       "      <td>admissible G-cover</td>\n",
       "      <td>\\nLet G be a finite group and let X→ S be a fa...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>light reduction pair;heavy reduction pair</td>\n",
       "      <td>\\n  Let $\\pi\\in\\fs_n$ and let $x,y$ be a pair ...</td>\n",
       "      <td>/home/shufan/que_tex/Post071005.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\n  Let π∈_n and let x,y be a pair of rooks th...</td>\n",
       "      <td>light reduction pair;heavy reduction pair</td>\n",
       "      <td>\\n  Let π∈_n and let x,y be a pair of rooks th...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O B_...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Local modification rule</td>\n",
       "      <td>\\label{lacma}  A \\emph{local modification rule...</td>\n",
       "      <td>/home/shufan/que_tex/hereditary_submit.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>A local modification rule is a pair (A,T), w...</td>\n",
       "      <td>Local modification rule</td>\n",
       "      <td>A B_MATH_TERM I_MATH_TERM I_MATH_TERM is a p...</td>\n",
       "      <td>O B_MATH_TERM I_MATH_TERM I_MATH_TERM O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Vertex sets</td>\n",
       "      <td>\\label{vertset}  A \\emph{vertex set} is any se...</td>\n",
       "      <td>/home/shufan/que_tex/hereditary_submit.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>A vertex set is any set which is at most cou...</td>\n",
       "      <td>Vertex sets</td>\n",
       "      <td>A vertex set is any set which is at most cou...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O B_MATH_TERM O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Palettes</td>\n",
       "      <td>A \\emph{finite palette} is a sequence $K = (K_...</td>\n",
       "      <td>/home/shufan/que_tex/hereditary_submit.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>A finite palette is a sequence K = (K_j)_j=0^∞...</td>\n",
       "      <td>Palettes</td>\n",
       "      <td>A finite palette is a sequence K = (K_j)_j=0^∞...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17837</th>\n",
       "      <td>preferred direction;special claw corresponding...</td>\n",
       "      <td>\\label{definition:SpecialClaw} Consider $\\lang...</td>\n",
       "      <td>/home/shufan/que_tex/CosetsVoltagesAndDerivedE...</td>\n",
       "      <td>definition + \\textit{}</td>\n",
       "      <td>Consider ⟨ G→ S, α→ A⟩, two adjacent vertices...</td>\n",
       "      <td>preferred direction;special claw corresponding...</td>\n",
       "      <td>Consider ⟨ G→ S, α→ A⟩, two adjacent vertices...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17844</th>\n",
       "      <td>Cyclicity classes</td>\n",
       "      <td>\\label{d:cyclasses}\\nAccording to Theorem~\\ref...</td>\n",
       "      <td>/home/shufan/que_tex/1307.3716.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>\\nAccording to Theorem &lt;ref&gt;, ^d has exactly d...</td>\n",
       "      <td>Cyclicity classes</td>\n",
       "      <td>\\nAccording to Theorem &lt;ref&gt;, ^d has exactly d...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17845</th>\n",
       "      <td>Wielandt number</td>\n",
       "      <td>By {\\em Wielandt number} we mean the following...</td>\n",
       "      <td>/home/shufan/que_tex/1307.3716.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>By Wielandt number we mean the following funct...</td>\n",
       "      <td>Wielandt number</td>\n",
       "      <td>By B_MATH_TERM I_MATH_TERM we mean the followi...</td>\n",
       "      <td>O B_MATH_TERM I_MATH_TERM O O O O O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17846</th>\n",
       "      <td>Girth</td>\n",
       "      <td>\\label{d:girth}\\nThe {\\em girth\\/} of $\\digr$,...</td>\n",
       "      <td>/home/shufan/que_tex/1307.3716.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>\\nThe girth of , denoted it by g(),\\nis the sm...</td>\n",
       "      <td>Girth</td>\n",
       "      <td>\\nThe B_MATH_TERM of , denoted it by g(),\\nis ...</td>\n",
       "      <td>O B_MATH_TERM O O O O O O O O O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17850</th>\n",
       "      <td>Critical graph</td>\n",
       "      <td>\\label{d:crit}\\nLet $A\\in\\Rpnn$. The cycles of...</td>\n",
       "      <td>/home/shufan/que_tex/1307.3716.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>\\nLet A∈. The cycles of (A) at which the maxim...</td>\n",
       "      <td>Critical graph</td>\n",
       "      <td>\\nLet A∈. The cycles of (A) at which the maxim...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>15191 rows × 8 columns</p>\n",
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      ],
      "text/plain": [
       "                                                    term  \\\n",
       "0                                   admissible $G$-cover   \n",
       "3              light reduction pair;heavy reduction pair   \n",
       "5                                Local modification rule   \n",
       "7                                            Vertex sets   \n",
       "8                                               Palettes   \n",
       "...                                                  ...   \n",
       "17837  preferred direction;special claw corresponding...   \n",
       "17844                                  Cyclicity classes   \n",
       "17845                                    Wielandt number   \n",
       "17846                                              Girth   \n",
       "17850                                     Critical graph   \n",
       "\n",
       "                                                     def  \\\n",
       "0      \\label{def_admissibleGcover}\\nLet $G$ be a fin...   \n",
       "3      \\n  Let $\\pi\\in\\fs_n$ and let $x,y$ be a pair ...   \n",
       "5      \\label{lacma}  A \\emph{local modification rule...   \n",
       "7      \\label{vertset}  A \\emph{vertex set} is any se...   \n",
       "8      A \\emph{finite palette} is a sequence $K = (K_...   \n",
       "...                                                  ...   \n",
       "17837  \\label{definition:SpecialClaw} Consider $\\lang...   \n",
       "17844  \\label{d:cyclasses}\\nAccording to Theorem~\\ref...   \n",
       "17845  By {\\em Wielandt number} we mean the following...   \n",
       "17846  \\label{d:girth}\\nThe {\\em girth\\/} of $\\digr$,...   \n",
       "17850  \\label{d:crit}\\nLet $A\\in\\Rpnn$. The cycles of...   \n",
       "\n",
       "                                               file_name  \\\n",
       "0       /home/shufan/que_tex/abelian_tropical_covers.tex   \n",
       "3                    /home/shufan/que_tex/Post071005.tex   \n",
       "5             /home/shufan/que_tex/hereditary_submit.tex   \n",
       "7             /home/shufan/que_tex/hereditary_submit.tex   \n",
       "8             /home/shufan/que_tex/hereditary_submit.tex   \n",
       "...                                                  ...   \n",
       "17837  /home/shufan/que_tex/CosetsVoltagesAndDerivedE...   \n",
       "17844                 /home/shufan/que_tex/1307.3716.tex   \n",
       "17845                 /home/shufan/que_tex/1307.3716.tex   \n",
       "17846                 /home/shufan/que_tex/1307.3716.tex   \n",
       "17850                 /home/shufan/que_tex/1307.3716.tex   \n",
       "\n",
       "              extraction_rule  \\\n",
       "0        definition + \\emph{}   \n",
       "3        definition + \\emph{}   \n",
       "5                definition[]   \n",
       "7                definition[]   \n",
       "8                definition[]   \n",
       "...                       ...   \n",
       "17837  definition + \\textit{}   \n",
       "17844            definition[]   \n",
       "17845            definition[]   \n",
       "17846            definition[]   \n",
       "17850            definition[]   \n",
       "\n",
       "                                          plain_text_def  \\\n",
       "0      \\nLet G be a finite group and let X→ S be a fa...   \n",
       "3      \\n  Let π∈_n and let x,y be a pair of rooks th...   \n",
       "5        A local modification rule is a pair (A,T), w...   \n",
       "7        A vertex set is any set which is at most cou...   \n",
       "8      A finite palette is a sequence K = (K_j)_j=0^∞...   \n",
       "...                                                  ...   \n",
       "17837   Consider ⟨ G→ S, α→ A⟩, two adjacent vertices...   \n",
       "17844  \\nAccording to Theorem <ref>, ^d has exactly d...   \n",
       "17845  By Wielandt number we mean the following funct...   \n",
       "17846  \\nThe girth of , denoted it by g(),\\nis the sm...   \n",
       "17850  \\nLet A∈. The cycles of (A) at which the maxim...   \n",
       "\n",
       "                                         plain_text_term  \\\n",
       "0                                     admissible G-cover   \n",
       "3              light reduction pair;heavy reduction pair   \n",
       "5                                Local modification rule   \n",
       "7                                            Vertex sets   \n",
       "8                                               Palettes   \n",
       "...                                                  ...   \n",
       "17837  preferred direction;special claw corresponding...   \n",
       "17844                                  Cyclicity classes   \n",
       "17845                                    Wielandt number   \n",
       "17846                                              Girth   \n",
       "17850                                     Critical graph   \n",
       "\n",
       "                                   masked_plain_text_def  \\\n",
       "0      \\nLet G be a finite group and let X→ S be a fa...   \n",
       "3      \\n  Let π∈_n and let x,y be a pair of rooks th...   \n",
       "5        A B_MATH_TERM I_MATH_TERM I_MATH_TERM is a p...   \n",
       "7        A vertex set is any set which is at most cou...   \n",
       "8      A finite palette is a sequence K = (K_j)_j=0^∞...   \n",
       "...                                                  ...   \n",
       "17837   Consider ⟨ G→ S, α→ A⟩, two adjacent vertices...   \n",
       "17844  \\nAccording to Theorem <ref>, ^d has exactly d...   \n",
       "17845  By B_MATH_TERM I_MATH_TERM we mean the followi...   \n",
       "17846  \\nThe B_MATH_TERM of , denoted it by g(),\\nis ...   \n",
       "17850  \\nLet A∈. The cycles of (A) at which the maxim...   \n",
       "\n",
       "                                             labeled_def  \n",
       "0      O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "3      O O O O O O O O O O O O O O O O O O O O O O B_...  \n",
       "5      O B_MATH_TERM I_MATH_TERM I_MATH_TERM O O O O ...  \n",
       "7      O O O O O O O O O O O O O O O O B_MATH_TERM O ...  \n",
       "8      O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "...                                                  ...  \n",
       "17837  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "17844  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "17845  O B_MATH_TERM I_MATH_TERM O O O O O O O O O O O O  \n",
       "17846      O B_MATH_TERM O O O O O O O O O O O O O O O O  \n",
       "17850  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "\n",
       "[15191 rows x 8 columns]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_clean = df_clean[~is_empty_or_only_whitespaces]\n",
    "df_clean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "16228959-b646-416d-b334-5f878c553012",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean = df_clean[~(df_clean['plain_text_term'].str.contains('�'))]\n",
    "df_clean = df_clean[~(df_clean['masked_plain_text_def'].str.contains('�'))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "05247d4b-30a3-4f55-90f3-6d6f765de37c",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>term</th>\n",
       "      <th>def</th>\n",
       "      <th>file_name</th>\n",
       "      <th>extraction_rule</th>\n",
       "      <th>plain_text_def</th>\n",
       "      <th>plain_text_term</th>\n",
       "      <th>masked_plain_text_def</th>\n",
       "      <th>labeled_def</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>109</th>\n",
       "      <td>$\\vect{k</td>\n",
       "      <td>\\nGiven a multigraded combinatorial Hopf algeb...</td>\n",
       "      <td>/home/shufan/que_tex/0910.5773.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nGiven a multigraded combinatorial Hopf algeb...</td>\n",
       "      <td>k</td>\n",
       "      <td>\\nGiven a multigraded combinatorial Hopf algeb...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>110</th>\n",
       "      <td>$\\vect{k</td>\n",
       "      <td>\\nGiven a multigraded combinatorial Hopf algeb...</td>\n",
       "      <td>/home/shufan/que_tex/0910.5773.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nGiven a multigraded combinatorial Hopf algeb...</td>\n",
       "      <td>k</td>\n",
       "      <td>\\nGiven a multigraded combinatorial Hopf algeb...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>477</th>\n",
       "      <td>$\\mathcal{X</td>\n",
       "      <td>[$\\mathcal{X}$-index] Let $\\mathcal{X}$ be a c...</td>\n",
       "      <td>/home/shufan/que_tex/SIA-index.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>[𝒳-index] Let 𝒳 be a class of matrices. The 𝒳-...</td>\n",
       "      <td>𝒳</td>\n",
       "      <td>[𝒳-index] Let 𝒳 be a class of matrices. The B_...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>651</th>\n",
       "      <td>$\\mathcal{A</td>\n",
       "      <td>\\nLet $L,U$ be subgroups of a group $G$ and $L...</td>\n",
       "      <td>/home/shufan/que_tex/1502.04615.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nLet L,U be subgroups of a group G and L be n...</td>\n",
       "      <td>𝒜</td>\n",
       "      <td>\\nLet L,U be subgroups of a group G and L be n...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>665</th>\n",
       "      <td>$\\mathcal{E</td>\n",
       "      <td>\\n If $\\mathcal{W}$ is any vector subspace of ...</td>\n",
       "      <td>/home/shufan/que_tex/JournalVersion.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\n If 𝒲 is any vector subspace of 𝒱, the ℰ-ann...</td>\n",
       "      <td>ℰ</td>\n",
       "      <td>\\n If 𝒲 is any vector subspace of 𝒱, the B_MAT...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1593</th>\n",
       "      <td>\\edg;\\edg;\\edg</td>\n",
       "      <td>\\label{thm:ladders-concentrate}\\nLet $M\\geq 3$...</td>\n",
       "      <td>/home/shufan/que_tex/trilongest.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet M≥ 3 and let 0&lt;δ&lt;1 be the constant from ...</td>\n",
       "      <td>;;</td>\n",
       "      <td>\\nLet M≥ 3 and let 0&lt;δ&lt;1 be the constant from ...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1594</th>\n",
       "      <td>\\edg;\\edg;\\edg;\\edg;\\edg;\\edg</td>\n",
       "      <td>\\label{def:ladders}\\n  [triangular ladders]\\nL...</td>\n",
       "      <td>/home/shufan/que_tex/trilongest.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\n  [triangular ladders]\\nLet Π⊂{ ,0,1}^* deno...</td>\n",
       "      <td>;;;;;</td>\n",
       "      <td>\\n  [triangular ladders]\\nLet Π⊂{B_MATH_TERM ,...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1595</th>\n",
       "      <td>\\edg;\\edg;\\edg;\\edg</td>\n",
       "      <td>[$f$-fan]\\label{def:fan}\\nFor $ f \\geq 3$, an ...</td>\n",
       "      <td>/home/shufan/que_tex/trilongest.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>[f-fan]\\nFor f ≥ 3, an f-fan at some vertex a&gt;...</td>\n",
       "      <td>;;;</td>\n",
       "      <td>[f-fan]\\nFor f ≥ 3, an f-fan at some vertex a&gt;...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1596</th>\n",
       "      <td>\\edg;\\edg;\\edg;\\edg;\\edg</td>\n",
       "      <td>\\label{def:M-bnd}[$M$-bounded triangular ladde...</td>\n",
       "      <td>/home/shufan/que_tex/trilongest.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>[M-bounded triangular ladders]\\nFor M≥3, defin...</td>\n",
       "      <td>;;;;</td>\n",
       "      <td>[M-bounded triangular ladders]\\nFor M≥3, defin...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1597</th>\n",
       "      <td>\\edg;\\edg;\\edg;\\edg;\\edg;\\edg</td>\n",
       "      <td>[boundary edges]\\label{def:boundary}\\nLet $ \\s...</td>\n",
       "      <td>/home/shufan/que_tex/trilongest.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>[boundary edges]\\nLet _π be an M-bounded trian...</td>\n",
       "      <td>;;;;;</td>\n",
       "      <td>[boundary edges]\\nLet _π be an M-bounded trian...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1770</th>\n",
       "      <td>\\</td>\n",
       "      <td>\\nFor $0\\leq \\ell \\leq m^{n},$ $k_{n,m}(\\ell )...</td>\n",
       "      <td>/home/shufan/que_tex/1802.08355.tex</td>\n",
       "      <td>definition + \\textit{}</td>\n",
       "      <td>\\nFor 0≤ℓ≤ m^n, k_n,m(ℓ ) is the number of\\nsu...</td>\n",
       "      <td></td>\n",
       "      <td>\\nFor 0≤ℓ≤ m^n, k_n,m(ℓ ) isB_MATH_TERMthe num...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1920</th>\n",
       "      <td>\\</td>\n",
       "      <td>\\n\\label{INTROOFRis}For every $i\\in\\{1,\\ldots,...</td>\n",
       "      <td>/home/shufan/que_tex/One_Sing.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nFor every i∈{1,…,ν} we introduce integers r_...</td>\n",
       "      <td></td>\n",
       "      <td>\\nFor every i∈{1,…,ν} we introduce integers r_...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2035</th>\n",
       "      <td>\\malg{S</td>\n",
       "      <td>\\label{def:S-mag alg}\\nLet $S$ be a subset of ...</td>\n",
       "      <td>/home/shufan/que_tex/0708.4191.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nLet S be a subset of ={2,3,…}. An S\\nA is a ...</td>\n",
       "      <td>S</td>\n",
       "      <td>\\nLet S be a subset of ={2,3,…}. An B_MATH_TER...</td>\n",
       "      <td>O O O O O O O O B_MATH_TERM O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2037</th>\n",
       "      <td>\\mcoalg{S</td>\n",
       "      <td>\\label{def:S-mag coalg}\\nLet $S\\subset \\NN$ be...</td>\n",
       "      <td>/home/shufan/que_tex/0708.4191.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nLet S⊂ be a subset. An S C is a\\nvector spac...</td>\n",
       "      <td>S</td>\n",
       "      <td>\\nLet S⊂ be a subset. An B_MATH_TERM C is a\\nv...</td>\n",
       "      <td>O O O O O O B_MATH_TERM O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2041</th>\n",
       "      <td>\\mbialg{T</td>\n",
       "      <td>\\label{def:T&lt;S mag bialg}\\nLet $T\\subset S\\sub...</td>\n",
       "      <td>/home/shufan/que_tex/0708.4191.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nLet T⊂ S⊂ be two sets. A TS\\n(,μ_n,Δ_n) is a...</td>\n",
       "      <td>T</td>\n",
       "      <td>\\nLet T⊂ S⊂ be two sets. A B_MATH_TERMS\\n(,μ_n...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2042</th>\n",
       "      <td>\\mrootalg{T</td>\n",
       "      <td>\\label{def:mag root algebra}\\nA \\emph{\\mrootal...</td>\n",
       "      <td>/home/shufan/que_tex/0708.4191.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nA TS A is an algebra over the free operad\\nT...</td>\n",
       "      <td>T</td>\n",
       "      <td>\\nA B_MATH_TERMS A is an algebra over the free...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2251</th>\n",
       "      <td>$\\PCA{n}$</td>\n",
       "      <td>The \\textit{Pascal cellular automaton} of dime...</td>\n",
       "      <td>/home/shufan/que_tex/BalancedSimplices.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>The Pascal cellular automaton of dimension n i...</td>\n",
       "      <td>n</td>\n",
       "      <td>The Pascal cellular automaton of dimension n i...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2680</th>\n",
       "      <td>$\\calL_{\\calH</td>\n",
       "      <td>\\label{templatedef}\\nAn $\\calL_{\\calH}$-struct...</td>\n",
       "      <td>/home/shufan/que_tex/TerryHPLS7-18.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nAn _-structure M with domain V is an _-templ...</td>\n",
       "      <td>_</td>\n",
       "      <td>\\nAn _-structure M with domain V is an B_MATH_...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2684</th>\n",
       "      <td>$\\mathcal{H</td>\n",
       "      <td>\\label{Hrand}\\n An $\\calL_{\\calH}$-structure $...</td>\n",
       "      <td>/home/shufan/que_tex/TerryHPLS7-18.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\n An _-structure M is ℋ-random if it is compl...</td>\n",
       "      <td>ℋ</td>\n",
       "      <td>\\n An _-structure M is B_MATH_TERM-random if i...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3028</th>\n",
       "      <td>$\\nn{N</td>\n",
       "      <td>An \\emph{$\\nn{N}$-graded minimal free resoluti...</td>\n",
       "      <td>/home/shufan/que_tex/1311.6291.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>An N-graded minimal free resolution of an N-gr...</td>\n",
       "      <td>N</td>\n",
       "      <td>An B_MATH_TERM-graded minimal free resolution ...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3464</th>\n",
       "      <td>$\\mathcal{H</td>\n",
       "      <td>\\label{def_Hconnected}\\nLet $N^u$ be a proper...</td>\n",
       "      <td>/home/shufan/que_tex/Fischer_et_al_Classes_of_...</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nLet N^u be a proper phylogenetic network on...</td>\n",
       "      <td>ℋ</td>\n",
       "      <td>\\nLet N^u be a proper phylogenetic network on...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3721</th>\n",
       "      <td>\\fmf\\</td>\n",
       "      <td>\\label{def:fmf}\\nLet $G$ be a quasisymmetric f...</td>\n",
       "      <td>/home/shufan/que_tex/1105.4212.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nLet G be a quasisymmetric function. Then we ...</td>\n",
       "      <td></td>\n",
       "      <td>\\nLet G be a quasisymmetric function. Then we ...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4385</th>\n",
       "      <td>$\\mathbf{g</td>\n",
       "      <td>\\nBy iterating the exchange relation (\\ref{exc...</td>\n",
       "      <td>/home/shufan/que_tex/markov_v2.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nBy iterating the exchange relation (&lt;ref&gt;) w...</td>\n",
       "      <td>𝐠</td>\n",
       "      <td>\\nBy iterating the exchange relation (&lt;ref&gt;) w...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4485</th>\n",
       "      <td>$\\widetilde{A</td>\n",
       "      <td>\\label{DefAffInv}\\nLet $\\sigma \\in \\widetilde{...</td>\n",
       "      <td>/home/shufan/que_tex/PosetV3.0.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nLet σ∈A_n and (a,b) ∈ [n] ×ℕ^*. We say that ...</td>\n",
       "      <td>A</td>\n",
       "      <td>\\nLet σ∈A_n and (a,b) ∈ [n] ×ℕ^*. We say that ...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4521</th>\n",
       "      <td>$\\RLk{k}$</td>\n",
       "      <td>Let $\\pi=\\pi_1 \\pi_2\\dots\\pi_n \\in \\mathcal{S}...</td>\n",
       "      <td>/home/shufan/que_tex/posets-jdt.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>Let π=π_1 π_2…π_n ∈𝒮_n. We say that π_i is a k...</td>\n",
       "      <td>k</td>\n",
       "      <td>Let π=π_1 π_2…π_n ∈𝒮_n. We say that π_i is a B...</td>\n",
       "      <td>O O O O O O O O O O B_MATH_TERM O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4618</th>\n",
       "      <td>$\\mathbb{Z</td>\n",
       "      <td>\\nLet $F$ and $G$ be faces of a full dimension...</td>\n",
       "      <td>/home/shufan/que_tex/1005.5158.tex</td>\n",
       "      <td>definition + \\textit{}</td>\n",
       "      <td>\\nLet F and G be faces of a full dimensional l...</td>\n",
       "      <td>ℤ</td>\n",
       "      <td>\\nLet F and G be faces of a full dimensional l...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4690</th>\n",
       "      <td>$\\mathcal{R</td>\n",
       "      <td>\\nLet $\\mathcal{R}$ be a class of retractions ...</td>\n",
       "      <td>/home/shufan/que_tex/0901.2621.tex</td>\n",
       "      <td>definition + \\textit{}</td>\n",
       "      <td>\\nLet ℛ be a class of retractions in the categ...</td>\n",
       "      <td>ℛ</td>\n",
       "      <td>\\nLet ℛ be a class of retractions in the categ...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6135</th>\n",
       "      <td>\\qr;\\pqr</td>\n",
       "      <td>\\n  \\label{D3}\\nA property of graphons $W$ is ...</td>\n",
       "      <td>/home/shufan/que_tex/1405.6808.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\n  \\nA property of graphons W is  if every gr...</td>\n",
       "      <td>;</td>\n",
       "      <td>\\n  \\nA property of graphons W is B_MATH_TERM ...</td>\n",
       "      <td>O O O O O O B_MATH_TERM O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6730</th>\n",
       "      <td>\\textbf{I</td>\n",
       "      <td>\\label{th:3.4}\\nLet $M$ be a mixed graph of or...</td>\n",
       "      <td>/home/shufan/que_tex/Hermitian-Randic_matrix_a...</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet M be a mixed graph of order n  and μ_1≥μ...</td>\n",
       "      <td>I</td>\n",
       "      <td>\\nLet M be a mixed graph of order n  and μ_1≥μ...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6906</th>\n",
       "      <td>$\\mathcal{P</td>\n",
       "      <td>[ \\emph{$\\mathcal{P}_{a,b}(\\zg)$, $\\mathcal{S...</td>\n",
       "      <td>/home/shufan/que_tex/MSW-Arxiv-June3.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>[ 𝒫_a,b(), 𝒮𝒫_a,b(^(p)), and 𝒞𝒫_a,b(^(pq))] \\...</td>\n",
       "      <td>𝒫</td>\n",
       "      <td>[ B_MATH_TERM_a,b(),𝒮𝒫_a,b(^(p)), and𝒞𝒫_a,b(^...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7181</th>\n",
       "      <td>\\textbf{x</td>\n",
       "      <td>\\label{vexp}Let $G$ be a graph equipped with v...</td>\n",
       "      <td>/home/shufan/que_tex/potts_activity.tex</td>\n",
       "      <td>theorem + \\textit{}</td>\n",
       "      <td>Let G be a graph equipped with vertex weights ...</td>\n",
       "      <td>x</td>\n",
       "      <td>Let G be a graph equipped with vertex weights ...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7182</th>\n",
       "      <td>\\textbf{x</td>\n",
       "      <td>\\label{statesumV} \\nLet $G$ be a graph equippe...</td>\n",
       "      <td>/home/shufan/que_tex/potts_activity.tex</td>\n",
       "      <td>theorem + \\textit{}</td>\n",
       "      <td>\\nLet G be a graph equipped with vertex weigh...</td>\n",
       "      <td>x</td>\n",
       "      <td>\\nLet G be a graph equipped with vertex weigh...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7183</th>\n",
       "      <td>\\textbf{x</td>\n",
       "      <td>\\label{forestV} \\nLet $G$ be a graph equipped ...</td>\n",
       "      <td>/home/shufan/que_tex/potts_activity.tex</td>\n",
       "      <td>theorem + \\textit{}</td>\n",
       "      <td>\\nLet G be a graph equipped with vertex weigh...</td>\n",
       "      <td>x</td>\n",
       "      <td>\\nLet G be a graph equipped with vertex weigh...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7188</th>\n",
       "      <td>$\\mathbf{x</td>\n",
       "      <td>\\label{def:xpf}\\nLet $\\mathbf{x} = (x_1,\\ldot...</td>\n",
       "      <td>/home/shufan/que_tex/parking_functions_tree_in...</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nLet 𝐱 = (x_1,…,x_n) ∈ℕ^n be some vector of ...</td>\n",
       "      <td>𝐱</td>\n",
       "      <td>\\nLet 𝐱 = (x_1,…,x_n) ∈ℕ^n be some vector of ...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7963</th>\n",
       "      <td>$\\mathbf{H</td>\n",
       "      <td>\\label{rank}\\nFor a connected hypergraph $\\mat...</td>\n",
       "      <td>/home/shufan/que_tex/1812.09770.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nFor a connected hypergraph 𝐇 the\\n𝐇-rank is ...</td>\n",
       "      <td>𝐇</td>\n",
       "      <td>\\nFor a connected hypergraph 𝐇 the\\nB_MATH_TER...</td>\n",
       "      <td>O O O O O O O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8069</th>\n",
       "      <td>$\\mathcal{U</td>\n",
       "      <td>\\nLet $R\\subset]0,n+1[\\times[0,1]$ be a simply...</td>\n",
       "      <td>/home/shufan/que_tex/DimerModelBeadModelAndSta...</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nLet R⊂]0,n+1[×[0,1] be a simply connected do...</td>\n",
       "      <td>𝒰</td>\n",
       "      <td>\\nLet R⊂]0,n+1[×[0,1] be a simply connected do...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9152</th>\n",
       "      <td>\\</td>\n",
       "      <td>\\n[The additional characteristic numbers $r_{i...</td>\n",
       "      <td>/home/shufan/que_tex/Index_3.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\n[The additional characteristic numbers r_i]F...</td>\n",
       "      <td></td>\n",
       "      <td>\\n[The additional characteristic numbers r_i]F...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9308</th>\n",
       "      <td>\\</td>\n",
       "      <td>\\nSuppose we are given a diagram $D$ of an ori...</td>\n",
       "      <td>/home/shufan/que_tex/forjktr.tex</td>\n",
       "      <td>definition + \\textit{}</td>\n",
       "      <td>\\nSuppose we are given a diagram D of an orien...</td>\n",
       "      <td></td>\n",
       "      <td>\\nSuppose we are given a diagram D of an orien...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9309</th>\n",
       "      <td>\\</td>\n",
       "      <td>\\nA \\emph{marked-graph}\\textit{\\ }$\\Omega.2$ \\...</td>\n",
       "      <td>/home/shufan/que_tex/forjktr.tex</td>\n",
       "      <td>definition + \\textit{}</td>\n",
       "      <td>\\nA marked-graph Ω.2 Reidemeister move is\\ncon...</td>\n",
       "      <td></td>\n",
       "      <td>\\nA marked-graphB_MATH_TERMΩ.2 Reidemeister mo...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9310</th>\n",
       "      <td>\\</td>\n",
       "      <td>\\n\\label{3move} A \\emph{marked-graph}\\textit{\\...</td>\n",
       "      <td>/home/shufan/que_tex/forjktr.tex</td>\n",
       "      <td>definition + \\textit{}</td>\n",
       "      <td>\\n A marked-graph Ω.3 Reidemeister\\nmove is ob...</td>\n",
       "      <td></td>\n",
       "      <td>\\n A marked-graphB_MATH_TERMΩ.3 Reidemeister\\n...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9346</th>\n",
       "      <td>$\\GL{3</td>\n",
       "      <td>\\label{def:SL3_equivalence} A\\n  \\emph{$\\GL{3}...</td>\n",
       "      <td>/home/shufan/que_tex/sigma12-094.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>A\\n  3-equivalence is an isomorphism ()^3 →\\n...</td>\n",
       "      <td>3</td>\n",
       "      <td>A\\n  B_MATH_TERM-equivalence is an isomorphis...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9380</th>\n",
       "      <td>\\NBRW;\\NBRW</td>\n",
       "      <td>\\n  \\label{thm-nbrw}\\n Let $G$ be a non-bipart...</td>\n",
       "      <td>/home/shufan/que_tex/ramanujan_arxiv_v5.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n  \\n Let G be a non-bipartite Ramanujan grap...</td>\n",
       "      <td>;</td>\n",
       "      <td>\\n  \\n Let G be a non-bipartite Ramanujan grap...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9519</th>\n",
       "      <td>PPP</td>\n",
       "      <td>A \\emph{periodic parallelogram polyomino} is a...</td>\n",
       "      <td>/home/shufan/que_tex/PPP_fpsac_2017.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>A periodic parallelogram polyomino is a parall...</td>\n",
       "      <td>PPP</td>\n",
       "      <td>A periodic parallelogram polyomino is a parall...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10591</th>\n",
       "      <td>\\</td>\n",
       "      <td>\\nIf the complex parameters $z_{1},\\ldots ,z_{...</td>\n",
       "      <td>/home/shufan/que_tex/1506.03596.tex</td>\n",
       "      <td>theorem + \\textit{}</td>\n",
       "      <td>\\nIf the complex parameters z_1,… ,z_n satisfy...</td>\n",
       "      <td></td>\n",
       "      <td>\\nIf the complex parameters z_1,… ,z_n satisfy...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11488</th>\n",
       "      <td>\\sol;\\sol;\\esol</td>\n",
       "      <td>\\nWe call a graph $G$ \\emph{\\sol} if deleting ...</td>\n",
       "      <td>/home/shufan/que_tex/EndsTanglesCrit.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nWe call a graph G  if deleting a finite set ...</td>\n",
       "      <td>;;</td>\n",
       "      <td>\\nWe call a graph G B_MATH_TERM if deleting a ...</td>\n",
       "      <td>O O O O O B_MATH_TERM O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12575</th>\n",
       "      <td>\\vol G</td>\n",
       "      <td>[Cheeger Inequality with vector norms of an ar...</td>\n",
       "      <td>/home/shufan/que_tex/LinearCheeger.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>[Cheeger Inequality with vector norms of an ar...</td>\n",
       "      <td>G</td>\n",
       "      <td>[Cheeger Inequality with vector norms of an ar...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12710</th>\n",
       "      <td>\\</td>\n",
       "      <td>\\n\\label{Theorem:polynomial-Gowers}Fix, for ev...</td>\n",
       "      <td>/home/shufan/que_tex/hales-jewett-gowers44.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nFix, for every i∈ k, a sequence (\\nx_i,n) _n...</td>\n",
       "      <td></td>\n",
       "      <td>\\nFix, for every i∈ k, a sequence (\\nx_i,n) _n...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13306</th>\n",
       "      <td>\\textbf{0</td>\n",
       "      <td>[Systems of functional equations~\\cite{DrmotaB...</td>\n",
       "      <td>/home/shufan/que_tex/Spanning_Trees.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>[Systems of functional equations &lt;cit.&gt;, simpl...</td>\n",
       "      <td>0</td>\n",
       "      <td>[Systems of functional equations &lt;cit.&gt;, simpl...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13615</th>\n",
       "      <td>\\reflectbox{L</td>\n",
       "      <td>\\label{prop:description of the Le-diagram of ...</td>\n",
       "      <td>/home/shufan/que_tex/Dyck_Paths_and_Positroids...</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n\\tA L-diagram L of type (n,2n) parameterize...</td>\n",
       "      <td>L</td>\n",
       "      <td>\\n\\tA B_MATH_TERM-diagram L of type (n,2n) pa...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16120</th>\n",
       "      <td>\\ltreetoldyck;\\ldycktoltree</td>\n",
       "      <td>\\n\\t$\\emph{\\ltreetoldyck}: \\ltree_n \\to \\ldyck...</td>\n",
       "      <td>/home/shufan/que_tex/2-columned_Final.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n\\t: _n →_n is a bijection and its inverse is...</td>\n",
       "      <td>;</td>\n",
       "      <td>\\n\\tB_MATH_TERM: _n →_n is a bijection and its...</td>\n",
       "      <td>O O O O O O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16121</th>\n",
       "      <td>\\ldycktoltree;\\prcttoldyck</td>\n",
       "      <td>\\label{thm:stat-preserving bijection}\\n\\t$ \\em...</td>\n",
       "      <td>/home/shufan/que_tex/2-columned_Final.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n\\t∘: ((2^n)) →_n is a bijection that maps th...</td>\n",
       "      <td>;</td>\n",
       "      <td>\\n\\tB_MATH_TERM∘ B_MATH_TERM: ((2^n)) →_n is a...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16239</th>\n",
       "      <td>\\cpl s</td>\n",
       "      <td>{\\rm \\cite{conicqodd}}\\Label{mainthmqodd} Let ...</td>\n",
       "      <td>/home/shufan/que_tex/1305.6673.tex</td>\n",
       "      <td>theorem + \\textit{}</td>\n",
       "      <td>&lt;cit.&gt;mainthmqodd Let  be the hyperplane at in...</td>\n",
       "      <td>s</td>\n",
       "      <td>&lt;cit.&gt;mainthmqodd Let  be the hyperplane at in...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16629</th>\n",
       "      <td>\\</td>\n",
       "      <td>\\n\\label{T : DiagGauss}Let $\\varphi =G$ be a c...</td>\n",
       "      <td>/home/shufan/que_tex/0811.1726.tex</td>\n",
       "      <td>theorem + \\textit{}</td>\n",
       "      <td>\\nLet φ =G be a centered Gaussian completely\\n...</td>\n",
       "      <td></td>\n",
       "      <td>\\nLet φ =G be a centered Gaussian completely\\n...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16631</th>\n",
       "      <td>\\</td>\n",
       "      <td>\\n\\label{D : Multipl}We say that the good comp...</td>\n",
       "      <td>/home/shufan/que_tex/0811.1726.tex</td>\n",
       "      <td>definition + \\textit{}</td>\n",
       "      <td>\\nWe say that the good completely random measu...</td>\n",
       "      <td></td>\n",
       "      <td>\\nWe say that the good completely random measu...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17034</th>\n",
       "      <td>${\\rm DD</td>\n",
       "      <td>\\t\\label{defn:DD}\\nIf $A \\in \\R^{d\\times d}$ s...</td>\n",
       "      <td>/home/shufan/que_tex/1211.3248.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\t\\nIf A ∈^d× d satisfies\\n|a_ij| ≤ε |a_ii|\\nf...</td>\n",
       "      <td>DD</td>\n",
       "      <td>\\t\\nIf A ∈^d× d satisfies\\n|a_ij| ≤ε |a_ii|\\nf...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O B_MATH_TER...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17419</th>\n",
       "      <td>$\\mathcal{F</td>\n",
       "      <td>\\nGiven a family $\\mathcal{F}$ of graphs, we s...</td>\n",
       "      <td>/home/shufan/que_tex/nondegenerate.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nGiven a family ℱ of graphs, we say that a gr...</td>\n",
       "      <td>ℱ</td>\n",
       "      <td>\\nGiven a family ℱ of graphs, we say that a gr...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17655</th>\n",
       "      <td>\\</td>\n",
       "      <td>\\nLet $\\sigma$ be an $N$-cone. Since the two i...</td>\n",
       "      <td>/home/shufan/que_tex/Twelveptthm.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nLet σ be an N-cone. Since the two integers p...</td>\n",
       "      <td></td>\n",
       "      <td>\\nLet σ be an N-cone. Since the two integers p...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17656</th>\n",
       "      <td>\\</td>\n",
       "      <td>\\n[The additional characteristic integers $r_{...</td>\n",
       "      <td>/home/shufan/que_tex/Twelveptthm.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\n[The additional characteristic integers r_i]...</td>\n",
       "      <td></td>\n",
       "      <td>\\n[The additional characteristic integers r_i]...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17797</th>\n",
       "      <td>$\\ex$;$\\Feven$</td>\n",
       "      <td>\\label{thm:edges}\\nFor every $r\\geq 2$ there e...</td>\n",
       "      <td>/home/shufan/que_tex/degreegirth11.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nFor every r≥ 2 there exists c=c(r)&gt;0 such th...</td>\n",
       "      <td>;</td>\n",
       "      <td>\\nFor every r≥ 2 there exists c=c(r)&gt;0 such th...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17798</th>\n",
       "      <td>$\\ex$;\\ex;\\ex</td>\n",
       "      <td>\\label{thm:deg}\\nLet $G$ be a graph with minim...</td>\n",
       "      <td>/home/shufan/que_tex/degreegirth11.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet G be a graph with minimum degree δ and (...</td>\n",
       "      <td>;;</td>\n",
       "      <td>\\nLet G be a graph with minimum degree δ and (...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                term  \\\n",
       "109                         $\\vect{k   \n",
       "110                         $\\vect{k   \n",
       "477                      $\\mathcal{X   \n",
       "651                      $\\mathcal{A   \n",
       "665                      $\\mathcal{E   \n",
       "1593                  \\edg;\\edg;\\edg   \n",
       "1594   \\edg;\\edg;\\edg;\\edg;\\edg;\\edg   \n",
       "1595             \\edg;\\edg;\\edg;\\edg   \n",
       "1596        \\edg;\\edg;\\edg;\\edg;\\edg   \n",
       "1597   \\edg;\\edg;\\edg;\\edg;\\edg;\\edg   \n",
       "1770                              \\    \n",
       "1920                              \\    \n",
       "2035                         \\malg{S   \n",
       "2037                       \\mcoalg{S   \n",
       "2041                       \\mbialg{T   \n",
       "2042                     \\mrootalg{T   \n",
       "2251                       $\\PCA{n}$   \n",
       "2680                   $\\calL_{\\calH   \n",
       "2684                     $\\mathcal{H   \n",
       "3028                          $\\nn{N   \n",
       "3464                     $\\mathcal{H   \n",
       "3721                          \\fmf\\    \n",
       "4385                      $\\mathbf{g   \n",
       "4485                   $\\widetilde{A   \n",
       "4521                       $\\RLk{k}$   \n",
       "4618                      $\\mathbb{Z   \n",
       "4690                     $\\mathcal{R   \n",
       "6135                        \\qr;\\pqr   \n",
       "6730                       \\textbf{I   \n",
       "6906                     $\\mathcal{P   \n",
       "7181                       \\textbf{x   \n",
       "7182                       \\textbf{x   \n",
       "7183                       \\textbf{x   \n",
       "7188                      $\\mathbf{x   \n",
       "7963                      $\\mathbf{H   \n",
       "8069                     $\\mathcal{U   \n",
       "9152                              \\    \n",
       "9308                              \\    \n",
       "9309                              \\    \n",
       "9310                              \\    \n",
       "9346                          $\\GL{3   \n",
       "9380                     \\NBRW;\\NBRW   \n",
       "9519                             PPP   \n",
       "10591                             \\    \n",
       "11488                \\sol;\\sol;\\esol   \n",
       "12575                         \\vol G   \n",
       "12710                             \\    \n",
       "13306                      \\textbf{0   \n",
       "13615                  \\reflectbox{L   \n",
       "16120    \\ltreetoldyck;\\ldycktoltree   \n",
       "16121     \\ldycktoltree;\\prcttoldyck   \n",
       "16239                         \\cpl s   \n",
       "16629                             \\    \n",
       "16631                             \\    \n",
       "17034                       ${\\rm DD   \n",
       "17419                    $\\mathcal{F   \n",
       "17655                             \\    \n",
       "17656                             \\    \n",
       "17797                 $\\ex$;$\\Feven$   \n",
       "17798                  $\\ex$;\\ex;\\ex   \n",
       "\n",
       "                                                     def  \\\n",
       "109    \\nGiven a multigraded combinatorial Hopf algeb...   \n",
       "110    \\nGiven a multigraded combinatorial Hopf algeb...   \n",
       "477    [$\\mathcal{X}$-index] Let $\\mathcal{X}$ be a c...   \n",
       "651    \\nLet $L,U$ be subgroups of a group $G$ and $L...   \n",
       "665    \\n If $\\mathcal{W}$ is any vector subspace of ...   \n",
       "1593   \\label{thm:ladders-concentrate}\\nLet $M\\geq 3$...   \n",
       "1594   \\label{def:ladders}\\n  [triangular ladders]\\nL...   \n",
       "1595   [$f$-fan]\\label{def:fan}\\nFor $ f \\geq 3$, an ...   \n",
       "1596   \\label{def:M-bnd}[$M$-bounded triangular ladde...   \n",
       "1597   [boundary edges]\\label{def:boundary}\\nLet $ \\s...   \n",
       "1770   \\nFor $0\\leq \\ell \\leq m^{n},$ $k_{n,m}(\\ell )...   \n",
       "1920   \\n\\label{INTROOFRis}For every $i\\in\\{1,\\ldots,...   \n",
       "2035   \\label{def:S-mag alg}\\nLet $S$ be a subset of ...   \n",
       "2037   \\label{def:S-mag coalg}\\nLet $S\\subset \\NN$ be...   \n",
       "2041   \\label{def:T<S mag bialg}\\nLet $T\\subset S\\sub...   \n",
       "2042   \\label{def:mag root algebra}\\nA \\emph{\\mrootal...   \n",
       "2251   The \\textit{Pascal cellular automaton} of dime...   \n",
       "2680   \\label{templatedef}\\nAn $\\calL_{\\calH}$-struct...   \n",
       "2684   \\label{Hrand}\\n An $\\calL_{\\calH}$-structure $...   \n",
       "3028   An \\emph{$\\nn{N}$-graded minimal free resoluti...   \n",
       "3464    \\label{def_Hconnected}\\nLet $N^u$ be a proper...   \n",
       "3721   \\label{def:fmf}\\nLet $G$ be a quasisymmetric f...   \n",
       "4385   \\nBy iterating the exchange relation (\\ref{exc...   \n",
       "4485   \\label{DefAffInv}\\nLet $\\sigma \\in \\widetilde{...   \n",
       "4521   Let $\\pi=\\pi_1 \\pi_2\\dots\\pi_n \\in \\mathcal{S}...   \n",
       "4618   \\nLet $F$ and $G$ be faces of a full dimension...   \n",
       "4690   \\nLet $\\mathcal{R}$ be a class of retractions ...   \n",
       "6135   \\n  \\label{D3}\\nA property of graphons $W$ is ...   \n",
       "6730   \\label{th:3.4}\\nLet $M$ be a mixed graph of or...   \n",
       "6906    [ \\emph{$\\mathcal{P}_{a,b}(\\zg)$, $\\mathcal{S...   \n",
       "7181   \\label{vexp}Let $G$ be a graph equipped with v...   \n",
       "7182   \\label{statesumV} \\nLet $G$ be a graph equippe...   \n",
       "7183   \\label{forestV} \\nLet $G$ be a graph equipped ...   \n",
       "7188    \\label{def:xpf}\\nLet $\\mathbf{x} = (x_1,\\ldot...   \n",
       "7963   \\label{rank}\\nFor a connected hypergraph $\\mat...   \n",
       "8069   \\nLet $R\\subset]0,n+1[\\times[0,1]$ be a simply...   \n",
       "9152   \\n[The additional characteristic numbers $r_{i...   \n",
       "9308   \\nSuppose we are given a diagram $D$ of an ori...   \n",
       "9309   \\nA \\emph{marked-graph}\\textit{\\ }$\\Omega.2$ \\...   \n",
       "9310   \\n\\label{3move} A \\emph{marked-graph}\\textit{\\...   \n",
       "9346   \\label{def:SL3_equivalence} A\\n  \\emph{$\\GL{3}...   \n",
       "9380   \\n  \\label{thm-nbrw}\\n Let $G$ be a non-bipart...   \n",
       "9519   A \\emph{periodic parallelogram polyomino} is a...   \n",
       "10591  \\nIf the complex parameters $z_{1},\\ldots ,z_{...   \n",
       "11488  \\nWe call a graph $G$ \\emph{\\sol} if deleting ...   \n",
       "12575  [Cheeger Inequality with vector norms of an ar...   \n",
       "12710  \\n\\label{Theorem:polynomial-Gowers}Fix, for ev...   \n",
       "13306  [Systems of functional equations~\\cite{DrmotaB...   \n",
       "13615   \\label{prop:description of the Le-diagram of ...   \n",
       "16120  \\n\\t$\\emph{\\ltreetoldyck}: \\ltree_n \\to \\ldyck...   \n",
       "16121  \\label{thm:stat-preserving bijection}\\n\\t$ \\em...   \n",
       "16239  {\\rm \\cite{conicqodd}}\\Label{mainthmqodd} Let ...   \n",
       "16629  \\n\\label{T : DiagGauss}Let $\\varphi =G$ be a c...   \n",
       "16631  \\n\\label{D : Multipl}We say that the good comp...   \n",
       "17034  \\t\\label{defn:DD}\\nIf $A \\in \\R^{d\\times d}$ s...   \n",
       "17419  \\nGiven a family $\\mathcal{F}$ of graphs, we s...   \n",
       "17655  \\nLet $\\sigma$ be an $N$-cone. Since the two i...   \n",
       "17656  \\n[The additional characteristic integers $r_{...   \n",
       "17797  \\label{thm:edges}\\nFor every $r\\geq 2$ there e...   \n",
       "17798  \\label{thm:deg}\\nLet $G$ be a graph with minim...   \n",
       "\n",
       "                                               file_name  \\\n",
       "109                   /home/shufan/que_tex/0910.5773.tex   \n",
       "110                   /home/shufan/que_tex/0910.5773.tex   \n",
       "477                   /home/shufan/que_tex/SIA-index.tex   \n",
       "651                  /home/shufan/que_tex/1502.04615.tex   \n",
       "665              /home/shufan/que_tex/JournalVersion.tex   \n",
       "1593                 /home/shufan/que_tex/trilongest.tex   \n",
       "1594                 /home/shufan/que_tex/trilongest.tex   \n",
       "1595                 /home/shufan/que_tex/trilongest.tex   \n",
       "1596                 /home/shufan/que_tex/trilongest.tex   \n",
       "1597                 /home/shufan/que_tex/trilongest.tex   \n",
       "1770                 /home/shufan/que_tex/1802.08355.tex   \n",
       "1920                   /home/shufan/que_tex/One_Sing.tex   \n",
       "2035                  /home/shufan/que_tex/0708.4191.tex   \n",
       "2037                  /home/shufan/que_tex/0708.4191.tex   \n",
       "2041                  /home/shufan/que_tex/0708.4191.tex   \n",
       "2042                  /home/shufan/que_tex/0708.4191.tex   \n",
       "2251          /home/shufan/que_tex/BalancedSimplices.tex   \n",
       "2680              /home/shufan/que_tex/TerryHPLS7-18.tex   \n",
       "2684              /home/shufan/que_tex/TerryHPLS7-18.tex   \n",
       "3028                  /home/shufan/que_tex/1311.6291.tex   \n",
       "3464   /home/shufan/que_tex/Fischer_et_al_Classes_of_...   \n",
       "3721                  /home/shufan/que_tex/1105.4212.tex   \n",
       "4385                  /home/shufan/que_tex/markov_v2.tex   \n",
       "4485                  /home/shufan/que_tex/PosetV3.0.tex   \n",
       "4521                 /home/shufan/que_tex/posets-jdt.tex   \n",
       "4618                  /home/shufan/que_tex/1005.5158.tex   \n",
       "4690                  /home/shufan/que_tex/0901.2621.tex   \n",
       "6135                  /home/shufan/que_tex/1405.6808.tex   \n",
       "6730   /home/shufan/que_tex/Hermitian-Randic_matrix_a...   \n",
       "6906            /home/shufan/que_tex/MSW-Arxiv-June3.tex   \n",
       "7181             /home/shufan/que_tex/potts_activity.tex   \n",
       "7182             /home/shufan/que_tex/potts_activity.tex   \n",
       "7183             /home/shufan/que_tex/potts_activity.tex   \n",
       "7188   /home/shufan/que_tex/parking_functions_tree_in...   \n",
       "7963                 /home/shufan/que_tex/1812.09770.tex   \n",
       "8069   /home/shufan/que_tex/DimerModelBeadModelAndSta...   \n",
       "9152                    /home/shufan/que_tex/Index_3.tex   \n",
       "9308                    /home/shufan/que_tex/forjktr.tex   \n",
       "9309                    /home/shufan/que_tex/forjktr.tex   \n",
       "9310                    /home/shufan/que_tex/forjktr.tex   \n",
       "9346                /home/shufan/que_tex/sigma12-094.tex   \n",
       "9380         /home/shufan/que_tex/ramanujan_arxiv_v5.tex   \n",
       "9519             /home/shufan/que_tex/PPP_fpsac_2017.tex   \n",
       "10591                /home/shufan/que_tex/1506.03596.tex   \n",
       "11488           /home/shufan/que_tex/EndsTanglesCrit.tex   \n",
       "12575             /home/shufan/que_tex/LinearCheeger.tex   \n",
       "12710     /home/shufan/que_tex/hales-jewett-gowers44.tex   \n",
       "13306            /home/shufan/que_tex/Spanning_Trees.tex   \n",
       "13615  /home/shufan/que_tex/Dyck_Paths_and_Positroids...   \n",
       "16120          /home/shufan/que_tex/2-columned_Final.tex   \n",
       "16121          /home/shufan/que_tex/2-columned_Final.tex   \n",
       "16239                 /home/shufan/que_tex/1305.6673.tex   \n",
       "16629                 /home/shufan/que_tex/0811.1726.tex   \n",
       "16631                 /home/shufan/que_tex/0811.1726.tex   \n",
       "17034                 /home/shufan/que_tex/1211.3248.tex   \n",
       "17419             /home/shufan/que_tex/nondegenerate.tex   \n",
       "17655               /home/shufan/que_tex/Twelveptthm.tex   \n",
       "17656               /home/shufan/que_tex/Twelveptthm.tex   \n",
       "17797             /home/shufan/que_tex/degreegirth11.tex   \n",
       "17798             /home/shufan/que_tex/degreegirth11.tex   \n",
       "\n",
       "              extraction_rule  \\\n",
       "109      definition + \\emph{}   \n",
       "110      definition + \\emph{}   \n",
       "477      definition + \\emph{}   \n",
       "651      definition + \\emph{}   \n",
       "665      definition + \\emph{}   \n",
       "1593        theorem + \\emph{}   \n",
       "1594     definition + \\emph{}   \n",
       "1595     definition + \\emph{}   \n",
       "1596     definition + \\emph{}   \n",
       "1597     definition + \\emph{}   \n",
       "1770   definition + \\textit{}   \n",
       "1920     definition + \\emph{}   \n",
       "2035     definition + \\emph{}   \n",
       "2037     definition + \\emph{}   \n",
       "2041     definition + \\emph{}   \n",
       "2042     definition + \\emph{}   \n",
       "2251             definition[]   \n",
       "2680     definition + \\emph{}   \n",
       "2684     definition + \\emph{}   \n",
       "3028     definition + \\emph{}   \n",
       "3464     definition + \\emph{}   \n",
       "3721     definition + \\emph{}   \n",
       "4385     definition + \\emph{}   \n",
       "4485     definition + \\emph{}   \n",
       "4521             definition[]   \n",
       "4618   definition + \\textit{}   \n",
       "4690   definition + \\textit{}   \n",
       "6135     definition + \\emph{}   \n",
       "6730        theorem + \\emph{}   \n",
       "6906     definition + \\emph{}   \n",
       "7181      theorem + \\textit{}   \n",
       "7182      theorem + \\textit{}   \n",
       "7183      theorem + \\textit{}   \n",
       "7188     definition + \\emph{}   \n",
       "7963     definition + \\emph{}   \n",
       "8069     definition + \\emph{}   \n",
       "9152     definition + \\emph{}   \n",
       "9308   definition + \\textit{}   \n",
       "9309   definition + \\textit{}   \n",
       "9310   definition + \\textit{}   \n",
       "9346     definition + \\emph{}   \n",
       "9380        theorem + \\emph{}   \n",
       "9519             definition[]   \n",
       "10591     theorem + \\textit{}   \n",
       "11488    definition + \\emph{}   \n",
       "12575       theorem + \\emph{}   \n",
       "12710       theorem + \\emph{}   \n",
       "13306       theorem + \\emph{}   \n",
       "13615       theorem + \\emph{}   \n",
       "16120       theorem + \\emph{}   \n",
       "16121       theorem + \\emph{}   \n",
       "16239     theorem + \\textit{}   \n",
       "16629     theorem + \\textit{}   \n",
       "16631  definition + \\textit{}   \n",
       "17034    definition + \\emph{}   \n",
       "17419    definition + \\emph{}   \n",
       "17655    definition + \\emph{}   \n",
       "17656    definition + \\emph{}   \n",
       "17797       theorem + \\emph{}   \n",
       "17798       theorem + \\emph{}   \n",
       "\n",
       "                                          plain_text_def plain_text_term  \\\n",
       "109    \\nGiven a multigraded combinatorial Hopf algeb...               k   \n",
       "110    \\nGiven a multigraded combinatorial Hopf algeb...               k   \n",
       "477    [𝒳-index] Let 𝒳 be a class of matrices. The 𝒳-...               𝒳   \n",
       "651    \\nLet L,U be subgroups of a group G and L be n...               𝒜   \n",
       "665    \\n If 𝒲 is any vector subspace of 𝒱, the ℰ-ann...               ℰ   \n",
       "1593   \\nLet M≥ 3 and let 0<δ<1 be the constant from ...              ;;   \n",
       "1594   \\n  [triangular ladders]\\nLet Π⊂{ ,0,1}^* deno...           ;;;;;   \n",
       "1595   [f-fan]\\nFor f ≥ 3, an f-fan at some vertex a>...             ;;;   \n",
       "1596   [M-bounded triangular ladders]\\nFor M≥3, defin...            ;;;;   \n",
       "1597   [boundary edges]\\nLet _π be an M-bounded trian...           ;;;;;   \n",
       "1770   \\nFor 0≤ℓ≤ m^n, k_n,m(ℓ ) is the number of\\nsu...                   \n",
       "1920   \\nFor every i∈{1,…,ν} we introduce integers r_...                   \n",
       "2035   \\nLet S be a subset of ={2,3,…}. An S\\nA is a ...               S   \n",
       "2037   \\nLet S⊂ be a subset. An S C is a\\nvector spac...               S   \n",
       "2041   \\nLet T⊂ S⊂ be two sets. A TS\\n(,μ_n,Δ_n) is a...               T   \n",
       "2042   \\nA TS A is an algebra over the free operad\\nT...               T   \n",
       "2251   The Pascal cellular automaton of dimension n i...               n   \n",
       "2680   \\nAn _-structure M with domain V is an _-templ...               _   \n",
       "2684   \\n An _-structure M is ℋ-random if it is compl...               ℋ   \n",
       "3028   An N-graded minimal free resolution of an N-gr...               N   \n",
       "3464    \\nLet N^u be a proper phylogenetic network on...               ℋ   \n",
       "3721   \\nLet G be a quasisymmetric function. Then we ...                   \n",
       "4385   \\nBy iterating the exchange relation (<ref>) w...               𝐠   \n",
       "4485   \\nLet σ∈A_n and (a,b) ∈ [n] ×ℕ^*. We say that ...               A   \n",
       "4521   Let π=π_1 π_2…π_n ∈𝒮_n. We say that π_i is a k...               k   \n",
       "4618   \\nLet F and G be faces of a full dimensional l...               ℤ   \n",
       "4690   \\nLet ℛ be a class of retractions in the categ...               ℛ   \n",
       "6135   \\n  \\nA property of graphons W is  if every gr...               ;   \n",
       "6730   \\nLet M be a mixed graph of order n  and μ_1≥μ...               I   \n",
       "6906    [ 𝒫_a,b(), 𝒮𝒫_a,b(^(p)), and 𝒞𝒫_a,b(^(pq))] \\...               𝒫   \n",
       "7181   Let G be a graph equipped with vertex weights ...               x   \n",
       "7182    \\nLet G be a graph equipped with vertex weigh...               x   \n",
       "7183    \\nLet G be a graph equipped with vertex weigh...               x   \n",
       "7188    \\nLet 𝐱 = (x_1,…,x_n) ∈ℕ^n be some vector of ...               𝐱   \n",
       "7963   \\nFor a connected hypergraph 𝐇 the\\n𝐇-rank is ...               𝐇   \n",
       "8069   \\nLet R⊂]0,n+1[×[0,1] be a simply connected do...               𝒰   \n",
       "9152   \\n[The additional characteristic numbers r_i]F...                   \n",
       "9308   \\nSuppose we are given a diagram D of an orien...                   \n",
       "9309   \\nA marked-graph Ω.2 Reidemeister move is\\ncon...                   \n",
       "9310   \\n A marked-graph Ω.3 Reidemeister\\nmove is ob...                   \n",
       "9346    A\\n  3-equivalence is an isomorphism ()^3 →\\n...               3   \n",
       "9380   \\n  \\n Let G be a non-bipartite Ramanujan grap...               ;   \n",
       "9519   A periodic parallelogram polyomino is a parall...             PPP   \n",
       "10591  \\nIf the complex parameters z_1,… ,z_n satisfy...                   \n",
       "11488  \\nWe call a graph G  if deleting a finite set ...              ;;   \n",
       "12575  [Cheeger Inequality with vector norms of an ar...               G   \n",
       "12710  \\nFix, for every i∈ k, a sequence (\\nx_i,n) _n...                   \n",
       "13306  [Systems of functional equations <cit.>, simpl...               0   \n",
       "13615   \\n\\tA L-diagram L of type (n,2n) parameterize...               L   \n",
       "16120  \\n\\t: _n →_n is a bijection and its inverse is...               ;   \n",
       "16121  \\n\\t∘: ((2^n)) →_n is a bijection that maps th...               ;   \n",
       "16239  <cit.>mainthmqodd Let  be the hyperplane at in...               s   \n",
       "16629  \\nLet φ =G be a centered Gaussian completely\\n...                   \n",
       "16631  \\nWe say that the good completely random measu...                   \n",
       "17034  \\t\\nIf A ∈^d× d satisfies\\n|a_ij| ≤ε |a_ii|\\nf...              DD   \n",
       "17419  \\nGiven a family ℱ of graphs, we say that a gr...               ℱ   \n",
       "17655  \\nLet σ be an N-cone. Since the two integers p...                   \n",
       "17656  \\n[The additional characteristic integers r_i]...                   \n",
       "17797  \\nFor every r≥ 2 there exists c=c(r)>0 such th...               ;   \n",
       "17798  \\nLet G be a graph with minimum degree δ and (...              ;;   \n",
       "\n",
       "                                   masked_plain_text_def  \\\n",
       "109    \\nGiven a multigraded combinatorial Hopf algeb...   \n",
       "110    \\nGiven a multigraded combinatorial Hopf algeb...   \n",
       "477    [𝒳-index] Let 𝒳 be a class of matrices. The B_...   \n",
       "651    \\nLet L,U be subgroups of a group G and L be n...   \n",
       "665    \\n If 𝒲 is any vector subspace of 𝒱, the B_MAT...   \n",
       "1593   \\nLet M≥ 3 and let 0<δ<1 be the constant from ...   \n",
       "1594   \\n  [triangular ladders]\\nLet Π⊂{B_MATH_TERM ,...   \n",
       "1595   [f-fan]\\nFor f ≥ 3, an f-fan at some vertex a>...   \n",
       "1596   [M-bounded triangular ladders]\\nFor M≥3, defin...   \n",
       "1597   [boundary edges]\\nLet _π be an M-bounded trian...   \n",
       "1770   \\nFor 0≤ℓ≤ m^n, k_n,m(ℓ ) isB_MATH_TERMthe num...   \n",
       "1920   \\nFor every i∈{1,…,ν} we introduce integers r_...   \n",
       "2035   \\nLet S be a subset of ={2,3,…}. An B_MATH_TER...   \n",
       "2037   \\nLet S⊂ be a subset. An B_MATH_TERM C is a\\nv...   \n",
       "2041   \\nLet T⊂ S⊂ be two sets. A B_MATH_TERMS\\n(,μ_n...   \n",
       "2042   \\nA B_MATH_TERMS A is an algebra over the free...   \n",
       "2251   The Pascal cellular automaton of dimension n i...   \n",
       "2680   \\nAn _-structure M with domain V is an B_MATH_...   \n",
       "2684   \\n An _-structure M is B_MATH_TERM-random if i...   \n",
       "3028   An B_MATH_TERM-graded minimal free resolution ...   \n",
       "3464    \\nLet N^u be a proper phylogenetic network on...   \n",
       "3721   \\nLet G be a quasisymmetric function. Then we ...   \n",
       "4385   \\nBy iterating the exchange relation (<ref>) w...   \n",
       "4485   \\nLet σ∈A_n and (a,b) ∈ [n] ×ℕ^*. We say that ...   \n",
       "4521   Let π=π_1 π_2…π_n ∈𝒮_n. We say that π_i is a B...   \n",
       "4618   \\nLet F and G be faces of a full dimensional l...   \n",
       "4690   \\nLet ℛ be a class of retractions in the categ...   \n",
       "6135   \\n  \\nA property of graphons W is B_MATH_TERM ...   \n",
       "6730   \\nLet M be a mixed graph of order n  and μ_1≥μ...   \n",
       "6906    [ B_MATH_TERM_a,b(),𝒮𝒫_a,b(^(p)), and𝒞𝒫_a,b(^...   \n",
       "7181   Let G be a graph equipped with vertex weights ...   \n",
       "7182    \\nLet G be a graph equipped with vertex weigh...   \n",
       "7183    \\nLet G be a graph equipped with vertex weigh...   \n",
       "7188    \\nLet 𝐱 = (x_1,…,x_n) ∈ℕ^n be some vector of ...   \n",
       "7963   \\nFor a connected hypergraph 𝐇 the\\nB_MATH_TER...   \n",
       "8069   \\nLet R⊂]0,n+1[×[0,1] be a simply connected do...   \n",
       "9152   \\n[The additional characteristic numbers r_i]F...   \n",
       "9308   \\nSuppose we are given a diagram D of an orien...   \n",
       "9309   \\nA marked-graphB_MATH_TERMΩ.2 Reidemeister mo...   \n",
       "9310   \\n A marked-graphB_MATH_TERMΩ.3 Reidemeister\\n...   \n",
       "9346    A\\n  B_MATH_TERM-equivalence is an isomorphis...   \n",
       "9380   \\n  \\n Let G be a non-bipartite Ramanujan grap...   \n",
       "9519   A periodic parallelogram polyomino is a parall...   \n",
       "10591  \\nIf the complex parameters z_1,… ,z_n satisfy...   \n",
       "11488  \\nWe call a graph G B_MATH_TERM if deleting a ...   \n",
       "12575  [Cheeger Inequality with vector norms of an ar...   \n",
       "12710  \\nFix, for every i∈ k, a sequence (\\nx_i,n) _n...   \n",
       "13306  [Systems of functional equations <cit.>, simpl...   \n",
       "13615   \\n\\tA B_MATH_TERM-diagram L of type (n,2n) pa...   \n",
       "16120  \\n\\tB_MATH_TERM: _n →_n is a bijection and its...   \n",
       "16121  \\n\\tB_MATH_TERM∘ B_MATH_TERM: ((2^n)) →_n is a...   \n",
       "16239  <cit.>mainthmqodd Let  be the hyperplane at in...   \n",
       "16629  \\nLet φ =G be a centered Gaussian completely\\n...   \n",
       "16631  \\nWe say that the good completely random measu...   \n",
       "17034  \\t\\nIf A ∈^d× d satisfies\\n|a_ij| ≤ε |a_ii|\\nf...   \n",
       "17419  \\nGiven a family ℱ of graphs, we say that a gr...   \n",
       "17655  \\nLet σ be an N-cone. Since the two integers p...   \n",
       "17656  \\n[The additional characteristic integers r_i]...   \n",
       "17797  \\nFor every r≥ 2 there exists c=c(r)>0 such th...   \n",
       "17798  \\nLet G be a graph with minimum degree δ and (...   \n",
       "\n",
       "                                             labeled_def  \n",
       "109    O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "110    O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "477    O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "651      O O O O O O O O O O O O O O O O O O O O O O O O  \n",
       "665            O O O O O O O O O O O O O O O O O O O O O  \n",
       "1593   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "1594   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "1595   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "1596   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "1597   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "1770                 O O O O O O O O O O O O O O O O O O  \n",
       "1920   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "2035   O O O O O O O O B_MATH_TERM O O O O O O O O O ...  \n",
       "2037   O O O O O O B_MATH_TERM O O O O O O O O O O O ...  \n",
       "2041   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "2042   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "2251   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "2680   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "2684                   O O O O O O O O O O O O O O O O O  \n",
       "3028   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "3464   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "3721         O O O O O O O O O O O O O O O O O O O O O O  \n",
       "4385   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "4485               O O O O O O O O O O O O O O O O O O O  \n",
       "4521   O O O O O O O O O O B_MATH_TERM O O O O O O O ...  \n",
       "4618   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "4690   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "6135   O O O O O O B_MATH_TERM O O O O O O O O O O O ...  \n",
       "6730   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "6906     O O O O O O O O O O O O O O O O O O O O O O O O  \n",
       "7181   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "7182   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "7183   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "7188   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "7963                         O O O O O O O O O O O O O O  \n",
       "8069   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "9152   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "9308   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "9309   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "9310   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "9346   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "9380   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "9519   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "10591  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "11488  O O O O O B_MATH_TERM O O O O O O O O O O O O ...  \n",
       "12575  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "12710  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "13306  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "13615  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "16120                          O O O O O O O O O O O O O  \n",
       "16121                  O O O O O O O O O O O O O O O O O  \n",
       "16239  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "16629  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "16631  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "17034  O O O O O O O O O O O O O O O O O O B_MATH_TER...  \n",
       "17419  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "17655  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "17656  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "17797                O O O O O O O O O O O O O O O O O O  \n",
       "17798  O O O O O O O O O O O O O O O O O O O O O O O ...  "
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_clean[df_clean['plain_text_term'].apply(lambda x: len(set(x)) == 1)]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "312be6b1-1a4b-4d9f-9e2b-b9ff8efecbb2",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean = df_clean[~df_clean['plain_text_term'].apply(lambda x: len(set(x)) == 1)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "396a82ef-1585-4412-9205-49d6ec75d9cc",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>term</th>\n",
       "      <th>def</th>\n",
       "      <th>file_name</th>\n",
       "      <th>extraction_rule</th>\n",
       "      <th>plain_text_def</th>\n",
       "      <th>plain_text_term</th>\n",
       "      <th>masked_plain_text_def</th>\n",
       "      <th>labeled_def</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>255</th>\n",
       "      <td>$\\mathcal{C;color-class-minimal</td>\n",
       "      <td>\\label{def:cc-min}\\n  Let $X=(V,E)$ be a hyper...</td>\n",
       "      <td>/home/shufan/que_tex/1709.10063.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\n  Let X=(V,E) be a hypergraph with color cla...</td>\n",
       "      <td>𝒞;𝒸ℴ𝓁ℴ𝓇-𝒸𝓁𝒶𝓈𝓈-𝓂𝒾𝓃𝒾𝓂𝒶𝓁</td>\n",
       "      <td>\\n  Let X=(V,E) be a hypergraph with color cla...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>542</th>\n",
       "      <td>$\\mathcal{U;$\\mathcal{U</td>\n",
       "      <td>\\n    Let $\\mathcal{U} = (U_1, \\dotsc, U_{p+q}...</td>\n",
       "      <td>/home/shufan/que_tex/CDMTaltogether7.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\n    Let 𝒰 = (U_1, …, U_p+q) be an ordered co...</td>\n",
       "      <td>𝒰;𝒰</td>\n",
       "      <td>\\n    Let 𝒰 = (U_1, …, U_p+q) be an ordered co...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>647</th>\n",
       "      <td>$\\mathcal{C;Cayley scheme</td>\n",
       "      <td>\\nLet $G$ be a finite group, $\\mathcal{R}$  a ...</td>\n",
       "      <td>/home/shufan/que_tex/1502.04615.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nLet G be a finite group, ℛ  a family of bina...</td>\n",
       "      <td>𝒞;𝒞𝒶𝓎𝓁ℯ𝓎 𝓈𝒸𝒽ℯ𝓂ℯ</td>\n",
       "      <td>\\nLet G be a finite group, ℛ  a family of bina...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O B_MATH_T...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1463</th>\n",
       "      <td>$\\DISC(\\delta)$</td>\n",
       "      <td>\\label{def:DISC_delta}\\n  Let~$0&lt;\\delta\\leq1$ ...</td>\n",
       "      <td>/home/shufan/que_tex/Fiedler.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>\\n  Let 0&lt;δ≤1 be given.  We say that an n-vert...</td>\n",
       "      <td>(δ)</td>\n",
       "      <td>\\n  Let 0&lt;δ≤1 be given.  We say that an n-vert...</td>\n",
       "      <td>O O O O O O O O O O O O O O B_MATH_TERM O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1464</th>\n",
       "      <td>$\\DISC_2(\\delta')$</td>\n",
       "      <td>\\label{def:DISC_2_delta}\\n  Let~$0&lt;\\delta'\\leq...</td>\n",
       "      <td>/home/shufan/que_tex/Fiedler.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>\\n  Let 0&lt;δ'≤1 be given.  We say that an n-ver...</td>\n",
       "      <td>_2(δ')</td>\n",
       "      <td>\\n  Let 0&lt;δ'≤1 be given.  We say that an n-ver...</td>\n",
       "      <td>O O O O O O O O O O O O O O B_MATH_TERM O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1465</th>\n",
       "      <td>$\\EIG(\\eps)$</td>\n",
       "      <td>\\label{def:EIG_epsilon}\\n  Let~$0&lt;\\eps\\leq1$ b...</td>\n",
       "      <td>/home/shufan/que_tex/Fiedler.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>\\n  Let 0&lt;≤1 be given.  We say that an n-verte...</td>\n",
       "      <td>()</td>\n",
       "      <td>\\n  Let 0&lt;≤1 be given.  We say that an n-verte...</td>\n",
       "      <td>O O O O O O O O O O O O O B_MATH_TERM O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1467</th>\n",
       "      <td>$\\ZINTDISC(\\rho;\\eta,\\sigma)$</td>\n",
       "      <td>\\label{def:Z-INT-DISC}\\n  For positive reals $...</td>\n",
       "      <td>/home/shufan/que_tex/Fiedler.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>\\n  For positive reals η and σ, we say that A\\...</td>\n",
       "      <td>(ρ;η,σ)</td>\n",
       "      <td>\\n  For positive reals η and σ, we say that A\\...</td>\n",
       "      <td>O O O O O O O O O O O B_MATH_TERM O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1468</th>\n",
       "      <td>$\\SINTDISC(\\chia;\\eta,\\sigma)$</td>\n",
       "      <td>\\label{def:S-INT-DISC}\\n  For positive reals $...</td>\n",
       "      <td>/home/shufan/que_tex/Fiedler.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>\\n  For positive reals η and σ, we say that A\\...</td>\n",
       "      <td>(;η,σ)</td>\n",
       "      <td>\\n  For positive reals η and σ, we say that A\\...</td>\n",
       "      <td>O O O O O O O O O O O B_MATH_TERM O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1478</th>\n",
       "      <td>$2$-$\\mathcal{M;$2$-$\\mathcal{NM</td>\n",
       "      <td>\\nLet $G$ be a $2$-edge-colored multigraph. We...</td>\n",
       "      <td>/home/shufan/que_tex/alternating-hamiltonian-c...</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nLet G be a 2-edge-colored multigraph. We say...</td>\n",
       "      <td>2-ℳ;2-𝒩ℳ</td>\n",
       "      <td>\\nLet G be a 2-edge-colored multigraph. We say...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1507</th>\n",
       "      <td>:;1;;1;;2.</td>\n",
       "      <td>[\\cite{LiPraeger}]\\n\\label{thm:LiPraeger}\\nLet...</td>\n",
       "      <td>/home/shufan/que_tex/1905.00520.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>[&lt;cit.&gt;]\\n\\nLet G be a finite permutation grou...</td>\n",
       "      <td>:;1;;1;;2.</td>\n",
       "      <td>[&lt;cit.&gt;]\\n\\nLet G be a finite permutation grou...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1657</th>\n",
       "      <td>(1);(2)</td>\n",
       "      <td>\\n\\begin{enumerate}[leftmargin=*]\\n\\item[ \\emp...</td>\n",
       "      <td>/home/shufan/que_tex/DeltaHiggsBonusRevisedFin...</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n\\n\\n   (1)  Let G be a unlooped simple graph...</td>\n",
       "      <td>(1);(2)</td>\n",
       "      <td>\\n\\n\\n   B_MATH_TERM  Let G be a unlooped simp...</td>\n",
       "      <td>B_MATH_TERM O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1658</th>\n",
       "      <td>(1);(2);(3);(4);(5)</td>\n",
       "      <td>\\label{thm:bouchetbinary}\\n  A delta-matroid i...</td>\n",
       "      <td>/home/shufan/que_tex/DeltaHiggsBonusRevisedFin...</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n  A delta-matroid is binary if and only if i...</td>\n",
       "      <td>(1);(2);(3);(4);(5)</td>\n",
       "      <td>\\n  A delta-matroid is binary if and only if i...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2295</th>\n",
       "      <td>$\\mathcal{O;$\\mathcal{C</td>\n",
       "      <td>\\nLet \\emph{$\\mathcal{O}(G)$} be all orientati...</td>\n",
       "      <td>/home/shufan/que_tex/arxivfile.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nLet 𝒪(G) be all orientations of G and 𝒞(G) b...</td>\n",
       "      <td>𝒪;𝒞</td>\n",
       "      <td>\\nLet B_MATH_TERM(G)be all orientations ofGand...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2401</th>\n",
       "      <td>\\d;\\d;\\d</td>\n",
       "      <td>[{\\cite[Theorem 6]{ZZ}}]\\label{T:zz}\\nSuppose ...</td>\n",
       "      <td>/home/shufan/que_tex/1310.3992.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>[&lt;cit.&gt;]\\nSuppose that  is a decreasing sequen...</td>\n",
       "      <td>;̣;̣ ̣</td>\n",
       "      <td>[&lt;cit.&gt;]\\nSuppose that B_MATH_TERM is a decrea...</td>\n",
       "      <td>O O O B_MATH_TERM O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2402</th>\n",
       "      <td>\\d;\\d;\\d</td>\n",
       "      <td>\\label{T:zz2}\\nSuppose that $\\emph{\\d}$ is a d...</td>\n",
       "      <td>/home/shufan/que_tex/1310.3992.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nSuppose that  is a decreasing sequence  of p...</td>\n",
       "      <td>;̣;̣ ̣</td>\n",
       "      <td>\\nSuppose that B_MATH_TERM is a decreasing seq...</td>\n",
       "      <td>O O B_MATH_TERM O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2707</th>\n",
       "      <td>$\\Hom_{\\leq 0</td>\n",
       "      <td>\\label{Hom0conf.def} \\cite{BRT}\\nAn object $X ...</td>\n",
       "      <td>/home/shufan/que_tex/1012.1276.tex</td>\n",
       "      <td>definition + \\textit{}</td>\n",
       "      <td>&lt;cit.&gt;\\nAn object X ∈^b (Q) is a _≤ 0 -config...</td>\n",
       "      <td>_≤ 0</td>\n",
       "      <td>&lt;cit.&gt;\\nAn object X ∈^b (Q) is a B_MATH_TERM ...</td>\n",
       "      <td>O O O O O O O O B_MATH_TERM O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3307</th>\n",
       "      <td>$(\\lambda,\\Pcal^{\\C</td>\n",
       "      <td>[ \\emph{Tangency conditions described by pairs...</td>\n",
       "      <td>/home/shufan/que_tex/0906.3828.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>[ Tangency conditions described by pairs of\\n ...</td>\n",
       "      <td>(λ,^</td>\n",
       "      <td>[ Tangency conditions described by pairs of\\n ...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3600</th>\n",
       "      <td>(1);(2);(3)</td>\n",
       "      <td>[Favaron \\cite{favaron:1986}]\\nA graph $G$ wit...</td>\n",
       "      <td>/home/shufan/que_tex/1501.07549.tex</td>\n",
       "      <td>theorem + \\textit{}</td>\n",
       "      <td>[Favaron &lt;cit.&gt;]\\nA graph G with vertex-connec...</td>\n",
       "      <td>(1);(2);(3)</td>\n",
       "      <td>[Favaron &lt;cit.&gt;]\\nA graph G with vertex-connec...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O B_...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3601</th>\n",
       "      <td>(1);(2)</td>\n",
       "      <td>[Favaron  \\cite{favaron:1986}]\\n\\label{thm:fav...</td>\n",
       "      <td>/home/shufan/que_tex/1501.07549.tex</td>\n",
       "      <td>theorem + \\textit{}</td>\n",
       "      <td>[Favaron  &lt;cit.&gt;]\\n\\n    Let G be a 2-connecte...</td>\n",
       "      <td>(1);(2)</td>\n",
       "      <td>[Favaron  &lt;cit.&gt;]\\n\\n    Let G be a 2-connecte...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3746</th>\n",
       "      <td>(\\v{C;(1);(2);(3)</td>\n",
       "      <td>\\label{ThC}\\n\\emph{(\\v{C}ada \\cite{C})} Let $G...</td>\n",
       "      <td>/home/shufan/que_tex/1409.3325.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n(Čada &lt;cit.&gt;) Let G be a claw-o-heavy graph....</td>\n",
       "      <td>(Č;̌(̌1̌)̌;̌(̌2̌)̌;̌(̌3̌)̌</td>\n",
       "      <td>\\nB_MATH_TERMada &lt;cit.&gt;) Let G be a claw-o-hea...</td>\n",
       "      <td>O O O O O O O O O B_MATH_TERM O O O O O O B_MA...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4053</th>\n",
       "      <td>$\\C^{\\circ</td>\n",
       "      <td>\\n\\label{def C0-compatible}\\nA collection $C$ ...</td>\n",
       "      <td>/home/shufan/que_tex/msw2_13.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\n\\nA collection C of arcs and essential loops...</td>\n",
       "      <td>^∘</td>\n",
       "      <td>\\n\\nA collection C of arcs and essential loops...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4778</th>\n",
       "      <td>(;);(;)</td>\n",
       "      <td>\\n\\label{thm:k_radius}\\nLet $k$ be a fixed pos...</td>\n",
       "      <td>/home/shufan/que_tex/k_radius_revised.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n\\nLet k be a fixed positive integer, and let...</td>\n",
       "      <td>(;);(;)</td>\n",
       "      <td>\\n\\nLet k be a fixed positive integer, and let...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4948</th>\n",
       "      <td>$\\mathfrak{P;$\\mathfrak{P;$\\mathfrak{P</td>\n",
       "      <td>\\nSuppose $\\mathfrak{P}=(\\Sigma, R, C)$ is a P...</td>\n",
       "      <td>/home/shufan/que_tex/1506.06476.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nSuppose 𝔓=(Σ, R, C) is a Parikh rewriting sy...</td>\n",
       "      <td>𝔓;𝔓;𝔓</td>\n",
       "      <td>\\nSuppose 𝔓=(Σ, R, C) is a Parikh rewriting sy...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6397</th>\n",
       "      <td>\\(\\mathbb{F;\\(\\mathbb{F;\\(\\mathbb{F</td>\n",
       "      <td>[Balanced tracking decomposition -- odd case]\\...</td>\n",
       "      <td>/home/shufan/que_tex/Pk-decomposition.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>[Balanced tracking decomposition – odd case]\\n...</td>\n",
       "      <td>𝔽;𝔽;𝔽</td>\n",
       "      <td>[Balanced tracking decomposition – odd case]\\n...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6398</th>\n",
       "      <td>\\(\\mathbb{F;\\(\\mathbb{F</td>\n",
       "      <td>[Balanced tracking decomposition -- even case]...</td>\n",
       "      <td>/home/shufan/que_tex/Pk-decomposition.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>[Balanced tracking decomposition – even case]\\...</td>\n",
       "      <td>𝔽;𝔽</td>\n",
       "      <td>[Balanced tracking decomposition – even case]\\...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6497</th>\n",
       "      <td>$\\mathcal{N;$\\mathcal{P</td>\n",
       "      <td>\\label{defNPposition}\\nLet $G$ and $H$ be gra...</td>\n",
       "      <td>/home/shufan/que_tex/1507.05673.tex</td>\n",
       "      <td>definition + \\textit{}</td>\n",
       "      <td>\\nLet G and H be graphs on which a combinator...</td>\n",
       "      <td>𝒩;𝒫</td>\n",
       "      <td>\\nLet G and H be graphs on which a combinator...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6566</th>\n",
       "      <td>$\\mD_\\cupC(\\irrFam)$</td>\n",
       "      <td>\\label{const:D}\\n       For a family of irredu...</td>\n",
       "      <td>/home/shufan/que_tex/Arxiv-1.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>\\n       For a family of irreducible intervals...</td>\n",
       "      <td>_()</td>\n",
       "      <td>\\n       For a family of irreducible intervals...</td>\n",
       "      <td>O O O O O O O O O B_MATH_TERM O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6567</th>\n",
       "      <td>$\\mR_\\cupC(\\irrFam)$</td>\n",
       "      <td>% and $\\irrFam_\\cupC(\\mR)$]\\n     \\label{const...</td>\n",
       "      <td>/home/shufan/que_tex/Arxiv-1.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>\\n     \\n       For a \\n       family of irred...</td>\n",
       "      <td>_()</td>\n",
       "      <td>\\n     \\n       For a \\n       family of irred...</td>\n",
       "      <td>O O O O O O O O O B_MATH_TERM O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6568</th>\n",
       "      <td>$\\Term(\\mR)$</td>\n",
       "      <td>\\label{def:Term}\\n     Let $\\Term(\\mR)$ be the...</td>\n",
       "      <td>/home/shufan/que_tex/Arxiv-1.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>\\n     Let () be the family of proper terminal...</td>\n",
       "      <td>()</td>\n",
       "      <td>\\n     Let B_MATH_TERM be the family of proper...</td>\n",
       "      <td>O B_MATH_TERM O O O O O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6685</th>\n",
       "      <td>$\\mathcal{P;$\\mathcal{P</td>\n",
       "      <td>\\label{partitions}\\n\\noindent\\n\\begin{enumera...</td>\n",
       "      <td>/home/shufan/que_tex/Adi_Avabis.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\n\\n\\n  * Let D be a digraph, and let 𝒫={P_1,...</td>\n",
       "      <td>𝒫;𝒫</td>\n",
       "      <td>\\n\\n\\n  * Let D be a digraph, and let 𝒫={P_1,...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7161</th>\n",
       "      <td>:;(1);(2);(3);(4)</td>\n",
       "      <td>\\label{thm:ekr}\\nFor all $0 &lt; \\eps &lt; 1$ there ...</td>\n",
       "      <td>/home/shufan/que_tex/ekr.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nFor all 0 &lt;  &lt; 1 there exists a constant C&gt;0...</td>\n",
       "      <td>:;(1);(2);(3);(4)</td>\n",
       "      <td>\\nFor all 0 &lt;  &lt; 1 there exists a constant C&gt;0...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7472</th>\n",
       "      <td>$\\mathcal{N;$\\mathcal{N;$\\mathcal{N</td>\n",
       "      <td>\\n  Let $\\mathcal{N}$ be a set of matroids, le...</td>\n",
       "      <td>/home/shufan/que_tex/stabifragirotaV5.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\n  Let 𝒩 be a set of matroids, let M be a mat...</td>\n",
       "      <td>𝒩;𝒩;𝒩</td>\n",
       "      <td>\\n  Let 𝒩 be a set of matroids, let M be a mat...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7750</th>\n",
       "      <td>94;215;205</td>\n",
       "      <td>\\n\\label{thm:resultssmallvalues}\\nThe values o...</td>\n",
       "      <td>/home/shufan/que_tex/SimpleArrangements.tex</td>\n",
       "      <td>theorem + \\textit{}</td>\n",
       "      <td>\\n\\nThe values of a_3^s(n), a_3^s(n), p_3^s(n)...</td>\n",
       "      <td>94;215;205</td>\n",
       "      <td>\\n\\nThe values of a_3^s(n), a_3^s(n), p_3^s(n)...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7913</th>\n",
       "      <td>$\\mathfrak{L;Hamilton-connected;$\\mathfrak{L;H...</td>\n",
       "      <td>\\label{def:monotonegraphpropertiesGlzetaandBGl...</td>\n",
       "      <td>/home/shufan/que_tex/HEINIGonprismsmoebiusladd...</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nLet 𝔏 be a map from graphs to subsets of _≥ ...</td>\n",
       "      <td>𝔏;ℌ𝔞𝔪𝔦𝔩𝔱𝔬𝔫-𝔠𝔬𝔫𝔫𝔢𝔠𝔱𝔢𝔡;𝔏;ℌ𝔞𝔪𝔦𝔩𝔱𝔬𝔫-𝔩𝔞𝔠𝔢𝔞𝔟𝔩𝔢;𝔟𝔦𝔭𝔞𝔯...</td>\n",
       "      <td>\\nLet 𝔏 be a map from graphs to subsets of _≥ ...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8035</th>\n",
       "      <td>(1);(;)</td>\n",
       "      <td>\\label{ind-stable}\\nAssume that $k, k_2, \\Del...</td>\n",
       "      <td>/home/shufan/que_tex/1102.3904.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nAssume that k, k_2, Δ are such that:\\n\\n\\n ...</td>\n",
       "      <td>(1);(;)</td>\n",
       "      <td>\\nAssume that k, k_2, Δ are such that:\\n\\n\\n ...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8110</th>\n",
       "      <td>размером</td>\n",
       "      <td>\\n\\tНазовем \\emph{размером} пары подмножеств $...</td>\n",
       "      <td>/home/shufan/que_tex/1602.08736.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\n\\tНазовем размером пары подмножеств (A, B) ∈...</td>\n",
       "      <td>размером</td>\n",
       "      <td>\\n\\tНазовем B_MATH_TERM пары подмножеств (A, B...</td>\n",
       "      <td>O B_MATH_TERM O O O O O O O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8530</th>\n",
       "      <td>[1]</td>\n",
       "      <td>\\n$\\emph{[1]}$ Let $s\\geq 2$ and $n\\geq 2$ be ...</td>\n",
       "      <td>/home/shufan/que_tex/RC11.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n[1] Let s≥ 2 and n≥ 2 be integers. If G is a...</td>\n",
       "      <td>[1]</td>\n",
       "      <td>\\nB_MATH_TERM Let s≥ 2 and n≥ 2 be integers. I...</td>\n",
       "      <td>B_MATH_TERM O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9477</th>\n",
       "      <td>если;если</td>\n",
       "      <td>\\label{hvector12k3}\\n Компоненты $h$-вектора м...</td>\n",
       "      <td>/home/shufan/que_tex/Melikhova_EV_On_the_numbe...</td>\n",
       "      <td>theorem + \\textit{}</td>\n",
       "      <td>\\n Компоненты h-вектора многогранника GZ(1  2^...</td>\n",
       "      <td>если;если</td>\n",
       "      <td>\\n Компоненты h-вектора многогранника GZ(1  2^...</td>\n",
       "      <td>O O O O O O O O O O O O O O B_MATH_TERM O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9925</th>\n",
       "      <td>\\NIM;\\NIM;$\\NIM(\\phi)$</td>\n",
       "      <td>\\label{thm-weakstab}\\n \\tFor any non-bipartite...</td>\n",
       "      <td>/home/shufan/que_tex/NIM-3rd-revision-0710.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n \\tFor any non-bipartite graphs H_i, i∈[k], ...</td>\n",
       "      <td>;;(ϕ)</td>\n",
       "      <td>\\n \\tFor any non-bipartite graphs H_i, i∈[k], ...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12726</th>\n",
       "      <td>\\d</td>\n",
       "      <td>[{\\cite{ZZ}}]\\label{T:ZZ7}\\nThe sequence  $\\em...</td>\n",
       "      <td>/home/shufan/que_tex/1403.6307.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>[&lt;cit.&gt;]\\nThe sequence   is bipartite graphic ...</td>\n",
       "      <td>̣</td>\n",
       "      <td>[&lt;cit.&gt;]\\nThe sequence  B_MATH_TERM is biparti...</td>\n",
       "      <td>O O O B_MATH_TERM O O O O O O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12727</th>\n",
       "      <td>\\d</td>\n",
       "      <td>\\label{T:ZZ7strongindices}\\nThe sequence  $\\em...</td>\n",
       "      <td>/home/shufan/que_tex/1403.6307.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nThe sequence    is bipartite graphic if and ...</td>\n",
       "      <td>̣</td>\n",
       "      <td>\\nThe sequence  B_MATH_TERM  is bipartite grap...</td>\n",
       "      <td>O O B_MATH_TERM O O O O O O O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13675</th>\n",
       "      <td>$\\mathcal{X;labeled $\\mathcal{X;$\\mathcal{X</td>\n",
       "      <td>\\label{Xseed}\\nLet $Q$ be a quiver with vertic...</td>\n",
       "      <td>/home/shufan/que_tex/ClusterFeb18-2019.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nLet Q be a quiver with vertices V,  associat...</td>\n",
       "      <td>𝒳;𝓁𝒶𝒷ℯ𝓁ℯ𝒹 𝒳;𝒳</td>\n",
       "      <td>\\nLet Q be a quiver with vertices V,  associat...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15601</th>\n",
       "      <td>$\\mathcal{Z;-partition</td>\n",
       "      <td>\\n\\label{def.ambivPp}Let $\\left(  P,\\gamma\\rig...</td>\n",
       "      <td>/home/shufan/que_tex/gzshuf2.tex</td>\n",
       "      <td>definition + \\textit{}</td>\n",
       "      <td>\\nLet (  P,γ) be a labeled poset. A\\n𝒵-enriche...</td>\n",
       "      <td>𝒵;-𝓅𝒶𝓇𝓉𝒾𝓉𝒾ℴ𝓃</td>\n",
       "      <td>\\nLet (  P,γ) be a labeled poset. A\\nB_MATH_TE...</td>\n",
       "      <td>O O O O O O O O O O B_MATH_TERM O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17087</th>\n",
       "      <td>$\\Gamma(\\C)$</td>\n",
       "      <td>The \\emph{polar complex} of a neural code $\\C$...</td>\n",
       "      <td>/home/shufan/que_tex/pierced_codes_revision.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>The polar complex of a neural code  is the sim...</td>\n",
       "      <td>Γ()</td>\n",
       "      <td>The polar complex of a neural code  is the sim...</td>\n",
       "      <td>O O O O O O O O O O O B_MATH_TERM O O O O O O ...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                    term  \\\n",
       "255                      $\\mathcal{C;color-class-minimal   \n",
       "542                              $\\mathcal{U;$\\mathcal{U   \n",
       "647                            $\\mathcal{C;Cayley scheme   \n",
       "1463                                     $\\DISC(\\delta)$   \n",
       "1464                                  $\\DISC_2(\\delta')$   \n",
       "1465                                        $\\EIG(\\eps)$   \n",
       "1467                       $\\ZINTDISC(\\rho;\\eta,\\sigma)$   \n",
       "1468                      $\\SINTDISC(\\chia;\\eta,\\sigma)$   \n",
       "1478                    $2$-$\\mathcal{M;$2$-$\\mathcal{NM   \n",
       "1507                                          :;1;;1;;2.   \n",
       "1657                                             (1);(2)   \n",
       "1658                                 (1);(2);(3);(4);(5)   \n",
       "2295                             $\\mathcal{O;$\\mathcal{C   \n",
       "2401                                            \\d;\\d;\\d   \n",
       "2402                                            \\d;\\d;\\d   \n",
       "2707                                       $\\Hom_{\\leq 0   \n",
       "3307                                 $(\\lambda,\\Pcal^{\\C   \n",
       "3600                                         (1);(2);(3)   \n",
       "3601                                             (1);(2)   \n",
       "3746                                   (\\v{C;(1);(2);(3)   \n",
       "4053                                          $\\C^{\\circ   \n",
       "4778                                             (;);(;)   \n",
       "4948              $\\mathfrak{P;$\\mathfrak{P;$\\mathfrak{P   \n",
       "6397                 \\(\\mathbb{F;\\(\\mathbb{F;\\(\\mathbb{F   \n",
       "6398                             \\(\\mathbb{F;\\(\\mathbb{F   \n",
       "6497                             $\\mathcal{N;$\\mathcal{P   \n",
       "6566                                $\\mD_\\cupC(\\irrFam)$   \n",
       "6567                                $\\mR_\\cupC(\\irrFam)$   \n",
       "6568                                        $\\Term(\\mR)$   \n",
       "6685                             $\\mathcal{P;$\\mathcal{P   \n",
       "7161                                   :;(1);(2);(3);(4)   \n",
       "7472                 $\\mathcal{N;$\\mathcal{N;$\\mathcal{N   \n",
       "7750                                          94;215;205   \n",
       "7913   $\\mathfrak{L;Hamilton-connected;$\\mathfrak{L;H...   \n",
       "8035                                             (1);(;)   \n",
       "8110                                            размером   \n",
       "8530                                                 [1]   \n",
       "9477                                           если;если   \n",
       "9925                              \\NIM;\\NIM;$\\NIM(\\phi)$   \n",
       "12726                                                 \\d   \n",
       "12727                                                 \\d   \n",
       "13675        $\\mathcal{X;labeled $\\mathcal{X;$\\mathcal{X   \n",
       "15601                             $\\mathcal{Z;-partition   \n",
       "17087                                       $\\Gamma(\\C)$   \n",
       "\n",
       "                                                     def  \\\n",
       "255    \\label{def:cc-min}\\n  Let $X=(V,E)$ be a hyper...   \n",
       "542    \\n    Let $\\mathcal{U} = (U_1, \\dotsc, U_{p+q}...   \n",
       "647    \\nLet $G$ be a finite group, $\\mathcal{R}$  a ...   \n",
       "1463   \\label{def:DISC_delta}\\n  Let~$0<\\delta\\leq1$ ...   \n",
       "1464   \\label{def:DISC_2_delta}\\n  Let~$0<\\delta'\\leq...   \n",
       "1465   \\label{def:EIG_epsilon}\\n  Let~$0<\\eps\\leq1$ b...   \n",
       "1467   \\label{def:Z-INT-DISC}\\n  For positive reals $...   \n",
       "1468   \\label{def:S-INT-DISC}\\n  For positive reals $...   \n",
       "1478   \\nLet $G$ be a $2$-edge-colored multigraph. We...   \n",
       "1507   [\\cite{LiPraeger}]\\n\\label{thm:LiPraeger}\\nLet...   \n",
       "1657   \\n\\begin{enumerate}[leftmargin=*]\\n\\item[ \\emp...   \n",
       "1658   \\label{thm:bouchetbinary}\\n  A delta-matroid i...   \n",
       "2295   \\nLet \\emph{$\\mathcal{O}(G)$} be all orientati...   \n",
       "2401   [{\\cite[Theorem 6]{ZZ}}]\\label{T:zz}\\nSuppose ...   \n",
       "2402   \\label{T:zz2}\\nSuppose that $\\emph{\\d}$ is a d...   \n",
       "2707   \\label{Hom0conf.def} \\cite{BRT}\\nAn object $X ...   \n",
       "3307   [ \\emph{Tangency conditions described by pairs...   \n",
       "3600   [Favaron \\cite{favaron:1986}]\\nA graph $G$ wit...   \n",
       "3601   [Favaron  \\cite{favaron:1986}]\\n\\label{thm:fav...   \n",
       "3746   \\label{ThC}\\n\\emph{(\\v{C}ada \\cite{C})} Let $G...   \n",
       "4053   \\n\\label{def C0-compatible}\\nA collection $C$ ...   \n",
       "4778   \\n\\label{thm:k_radius}\\nLet $k$ be a fixed pos...   \n",
       "4948   \\nSuppose $\\mathfrak{P}=(\\Sigma, R, C)$ is a P...   \n",
       "6397   [Balanced tracking decomposition -- odd case]\\...   \n",
       "6398   [Balanced tracking decomposition -- even case]...   \n",
       "6497    \\label{defNPposition}\\nLet $G$ and $H$ be gra...   \n",
       "6566   \\label{const:D}\\n       For a family of irredu...   \n",
       "6567   % and $\\irrFam_\\cupC(\\mR)$]\\n     \\label{const...   \n",
       "6568   \\label{def:Term}\\n     Let $\\Term(\\mR)$ be the...   \n",
       "6685    \\label{partitions}\\n\\noindent\\n\\begin{enumera...   \n",
       "7161   \\label{thm:ekr}\\nFor all $0 < \\eps < 1$ there ...   \n",
       "7472   \\n  Let $\\mathcal{N}$ be a set of matroids, le...   \n",
       "7750   \\n\\label{thm:resultssmallvalues}\\nThe values o...   \n",
       "7913   \\label{def:monotonegraphpropertiesGlzetaandBGl...   \n",
       "8035    \\label{ind-stable}\\nAssume that $k, k_2, \\Del...   \n",
       "8110   \\n\\tНазовем \\emph{размером} пары подмножеств $...   \n",
       "8530   \\n$\\emph{[1]}$ Let $s\\geq 2$ and $n\\geq 2$ be ...   \n",
       "9477   \\label{hvector12k3}\\n Компоненты $h$-вектора м...   \n",
       "9925   \\label{thm-weakstab}\\n \\tFor any non-bipartite...   \n",
       "12726  [{\\cite{ZZ}}]\\label{T:ZZ7}\\nThe sequence  $\\em...   \n",
       "12727  \\label{T:ZZ7strongindices}\\nThe sequence  $\\em...   \n",
       "13675  \\label{Xseed}\\nLet $Q$ be a quiver with vertic...   \n",
       "15601  \\n\\label{def.ambivPp}Let $\\left(  P,\\gamma\\rig...   \n",
       "17087  The \\emph{polar complex} of a neural code $\\C$...   \n",
       "\n",
       "                                               file_name  \\\n",
       "255                  /home/shufan/que_tex/1709.10063.tex   \n",
       "542             /home/shufan/que_tex/CDMTaltogether7.tex   \n",
       "647                  /home/shufan/que_tex/1502.04615.tex   \n",
       "1463                    /home/shufan/que_tex/Fiedler.tex   \n",
       "1464                    /home/shufan/que_tex/Fiedler.tex   \n",
       "1465                    /home/shufan/que_tex/Fiedler.tex   \n",
       "1467                    /home/shufan/que_tex/Fiedler.tex   \n",
       "1468                    /home/shufan/que_tex/Fiedler.tex   \n",
       "1478   /home/shufan/que_tex/alternating-hamiltonian-c...   \n",
       "1507                 /home/shufan/que_tex/1905.00520.tex   \n",
       "1657   /home/shufan/que_tex/DeltaHiggsBonusRevisedFin...   \n",
       "1658   /home/shufan/que_tex/DeltaHiggsBonusRevisedFin...   \n",
       "2295                  /home/shufan/que_tex/arxivfile.tex   \n",
       "2401                  /home/shufan/que_tex/1310.3992.tex   \n",
       "2402                  /home/shufan/que_tex/1310.3992.tex   \n",
       "2707                  /home/shufan/que_tex/1012.1276.tex   \n",
       "3307                  /home/shufan/que_tex/0906.3828.tex   \n",
       "3600                 /home/shufan/que_tex/1501.07549.tex   \n",
       "3601                 /home/shufan/que_tex/1501.07549.tex   \n",
       "3746                  /home/shufan/que_tex/1409.3325.tex   \n",
       "4053                    /home/shufan/que_tex/msw2_13.tex   \n",
       "4778           /home/shufan/que_tex/k_radius_revised.tex   \n",
       "4948                 /home/shufan/que_tex/1506.06476.tex   \n",
       "6397           /home/shufan/que_tex/Pk-decomposition.tex   \n",
       "6398           /home/shufan/que_tex/Pk-decomposition.tex   \n",
       "6497                 /home/shufan/que_tex/1507.05673.tex   \n",
       "6566                    /home/shufan/que_tex/Arxiv-1.tex   \n",
       "6567                    /home/shufan/que_tex/Arxiv-1.tex   \n",
       "6568                    /home/shufan/que_tex/Arxiv-1.tex   \n",
       "6685                 /home/shufan/que_tex/Adi_Avabis.tex   \n",
       "7161                        /home/shufan/que_tex/ekr.tex   \n",
       "7472           /home/shufan/que_tex/stabifragirotaV5.tex   \n",
       "7750         /home/shufan/que_tex/SimpleArrangements.tex   \n",
       "7913   /home/shufan/que_tex/HEINIGonprismsmoebiusladd...   \n",
       "8035                  /home/shufan/que_tex/1102.3904.tex   \n",
       "8110                 /home/shufan/que_tex/1602.08736.tex   \n",
       "8530                       /home/shufan/que_tex/RC11.tex   \n",
       "9477   /home/shufan/que_tex/Melikhova_EV_On_the_numbe...   \n",
       "9925      /home/shufan/que_tex/NIM-3rd-revision-0710.tex   \n",
       "12726                 /home/shufan/que_tex/1403.6307.tex   \n",
       "12727                 /home/shufan/que_tex/1403.6307.tex   \n",
       "13675         /home/shufan/que_tex/ClusterFeb18-2019.tex   \n",
       "15601                   /home/shufan/que_tex/gzshuf2.tex   \n",
       "17087    /home/shufan/que_tex/pierced_codes_revision.tex   \n",
       "\n",
       "              extraction_rule  \\\n",
       "255      definition + \\emph{}   \n",
       "542      definition + \\emph{}   \n",
       "647      definition + \\emph{}   \n",
       "1463             definition[]   \n",
       "1464             definition[]   \n",
       "1465             definition[]   \n",
       "1467             definition[]   \n",
       "1468             definition[]   \n",
       "1478     definition + \\emph{}   \n",
       "1507        theorem + \\emph{}   \n",
       "1657        theorem + \\emph{}   \n",
       "1658        theorem + \\emph{}   \n",
       "2295     definition + \\emph{}   \n",
       "2401        theorem + \\emph{}   \n",
       "2402        theorem + \\emph{}   \n",
       "2707   definition + \\textit{}   \n",
       "3307     definition + \\emph{}   \n",
       "3600      theorem + \\textit{}   \n",
       "3601      theorem + \\textit{}   \n",
       "3746        theorem + \\emph{}   \n",
       "4053     definition + \\emph{}   \n",
       "4778        theorem + \\emph{}   \n",
       "4948     definition + \\emph{}   \n",
       "6397     definition + \\emph{}   \n",
       "6398     definition + \\emph{}   \n",
       "6497   definition + \\textit{}   \n",
       "6566             definition[]   \n",
       "6567             definition[]   \n",
       "6568             definition[]   \n",
       "6685     definition + \\emph{}   \n",
       "7161        theorem + \\emph{}   \n",
       "7472     definition + \\emph{}   \n",
       "7750      theorem + \\textit{}   \n",
       "7913     definition + \\emph{}   \n",
       "8035        theorem + \\emph{}   \n",
       "8110     definition + \\emph{}   \n",
       "8530        theorem + \\emph{}   \n",
       "9477      theorem + \\textit{}   \n",
       "9925        theorem + \\emph{}   \n",
       "12726       theorem + \\emph{}   \n",
       "12727       theorem + \\emph{}   \n",
       "13675    definition + \\emph{}   \n",
       "15601  definition + \\textit{}   \n",
       "17087            definition[]   \n",
       "\n",
       "                                          plain_text_def  \\\n",
       "255    \\n  Let X=(V,E) be a hypergraph with color cla...   \n",
       "542    \\n    Let 𝒰 = (U_1, …, U_p+q) be an ordered co...   \n",
       "647    \\nLet G be a finite group, ℛ  a family of bina...   \n",
       "1463   \\n  Let 0<δ≤1 be given.  We say that an n-vert...   \n",
       "1464   \\n  Let 0<δ'≤1 be given.  We say that an n-ver...   \n",
       "1465   \\n  Let 0<≤1 be given.  We say that an n-verte...   \n",
       "1467   \\n  For positive reals η and σ, we say that A\\...   \n",
       "1468   \\n  For positive reals η and σ, we say that A\\...   \n",
       "1478   \\nLet G be a 2-edge-colored multigraph. We say...   \n",
       "1507   [<cit.>]\\n\\nLet G be a finite permutation grou...   \n",
       "1657   \\n\\n\\n   (1)  Let G be a unlooped simple graph...   \n",
       "1658   \\n  A delta-matroid is binary if and only if i...   \n",
       "2295   \\nLet 𝒪(G) be all orientations of G and 𝒞(G) b...   \n",
       "2401   [<cit.>]\\nSuppose that  is a decreasing sequen...   \n",
       "2402   \\nSuppose that  is a decreasing sequence  of p...   \n",
       "2707    <cit.>\\nAn object X ∈^b (Q) is a _≤ 0 -config...   \n",
       "3307   [ Tangency conditions described by pairs of\\n ...   \n",
       "3600   [Favaron <cit.>]\\nA graph G with vertex-connec...   \n",
       "3601   [Favaron  <cit.>]\\n\\n    Let G be a 2-connecte...   \n",
       "3746   \\n(Čada <cit.>) Let G be a claw-o-heavy graph....   \n",
       "4053   \\n\\nA collection C of arcs and essential loops...   \n",
       "4778   \\n\\nLet k be a fixed positive integer, and let...   \n",
       "4948   \\nSuppose 𝔓=(Σ, R, C) is a Parikh rewriting sy...   \n",
       "6397   [Balanced tracking decomposition – odd case]\\n...   \n",
       "6398   [Balanced tracking decomposition – even case]\\...   \n",
       "6497    \\nLet G and H be graphs on which a combinator...   \n",
       "6566   \\n       For a family of irreducible intervals...   \n",
       "6567   \\n     \\n       For a \\n       family of irred...   \n",
       "6568   \\n     Let () be the family of proper terminal...   \n",
       "6685    \\n\\n\\n  * Let D be a digraph, and let 𝒫={P_1,...   \n",
       "7161   \\nFor all 0 <  < 1 there exists a constant C>0...   \n",
       "7472   \\n  Let 𝒩 be a set of matroids, let M be a mat...   \n",
       "7750   \\n\\nThe values of a_3^s(n), a_3^s(n), p_3^s(n)...   \n",
       "7913   \\nLet 𝔏 be a map from graphs to subsets of _≥ ...   \n",
       "8035    \\nAssume that k, k_2, Δ are such that:\\n\\n\\n ...   \n",
       "8110   \\n\\tНазовем размером пары подмножеств (A, B) ∈...   \n",
       "8530   \\n[1] Let s≥ 2 and n≥ 2 be integers. If G is a...   \n",
       "9477   \\n Компоненты h-вектора многогранника GZ(1  2^...   \n",
       "9925   \\n \\tFor any non-bipartite graphs H_i, i∈[k], ...   \n",
       "12726  [<cit.>]\\nThe sequence   is bipartite graphic ...   \n",
       "12727  \\nThe sequence    is bipartite graphic if and ...   \n",
       "13675  \\nLet Q be a quiver with vertices V,  associat...   \n",
       "15601  \\nLet (  P,γ) be a labeled poset. A\\n𝒵-enriche...   \n",
       "17087  The polar complex of a neural code  is the sim...   \n",
       "\n",
       "                                         plain_text_term  \\\n",
       "255                                𝒞;𝒸ℴ𝓁ℴ𝓇-𝒸𝓁𝒶𝓈𝓈-𝓂𝒾𝓃𝒾𝓂𝒶𝓁   \n",
       "542                                                  𝒰;𝒰   \n",
       "647                                      𝒞;𝒞𝒶𝓎𝓁ℯ𝓎 𝓈𝒸𝒽ℯ𝓂ℯ   \n",
       "1463                                                 (δ)   \n",
       "1464                                              _2(δ')   \n",
       "1465                                                  ()   \n",
       "1467                                             (ρ;η,σ)   \n",
       "1468                                              (;η,σ)   \n",
       "1478                                            2-ℳ;2-𝒩ℳ   \n",
       "1507                                          :;1;;1;;2.   \n",
       "1657                                             (1);(2)   \n",
       "1658                                 (1);(2);(3);(4);(5)   \n",
       "2295                                                 𝒪;𝒞   \n",
       "2401                                              ;̣;̣ ̣   \n",
       "2402                                              ;̣;̣ ̣   \n",
       "2707                                                _≤ 0   \n",
       "3307                                                (λ,^   \n",
       "3600                                         (1);(2);(3)   \n",
       "3601                                             (1);(2)   \n",
       "3746                          (Č;̌(̌1̌)̌;̌(̌2̌)̌;̌(̌3̌)̌   \n",
       "4053                                                  ^∘   \n",
       "4778                                             (;);(;)   \n",
       "4948                                               𝔓;𝔓;𝔓   \n",
       "6397                                               𝔽;𝔽;𝔽   \n",
       "6398                                                 𝔽;𝔽   \n",
       "6497                                                 𝒩;𝒫   \n",
       "6566                                                 _()   \n",
       "6567                                                 _()   \n",
       "6568                                                  ()   \n",
       "6685                                                 𝒫;𝒫   \n",
       "7161                                   :;(1);(2);(3);(4)   \n",
       "7472                                               𝒩;𝒩;𝒩   \n",
       "7750                                          94;215;205   \n",
       "7913   𝔏;ℌ𝔞𝔪𝔦𝔩𝔱𝔬𝔫-𝔠𝔬𝔫𝔫𝔢𝔠𝔱𝔢𝔡;𝔏;ℌ𝔞𝔪𝔦𝔩𝔱𝔬𝔫-𝔩𝔞𝔠𝔢𝔞𝔟𝔩𝔢;𝔟𝔦𝔭𝔞𝔯...   \n",
       "8035                                             (1);(;)   \n",
       "8110                                            размером   \n",
       "8530                                                 [1]   \n",
       "9477                                           если;если   \n",
       "9925                                               ;;(ϕ)   \n",
       "12726                                                  ̣   \n",
       "12727                                                  ̣   \n",
       "13675                                      𝒳;𝓁𝒶𝒷ℯ𝓁ℯ𝒹 𝒳;𝒳   \n",
       "15601                                       𝒵;-𝓅𝒶𝓇𝓉𝒾𝓉𝒾ℴ𝓃   \n",
       "17087                                                Γ()   \n",
       "\n",
       "                                   masked_plain_text_def  \\\n",
       "255    \\n  Let X=(V,E) be a hypergraph with color cla...   \n",
       "542    \\n    Let 𝒰 = (U_1, …, U_p+q) be an ordered co...   \n",
       "647    \\nLet G be a finite group, ℛ  a family of bina...   \n",
       "1463   \\n  Let 0<δ≤1 be given.  We say that an n-vert...   \n",
       "1464   \\n  Let 0<δ'≤1 be given.  We say that an n-ver...   \n",
       "1465   \\n  Let 0<≤1 be given.  We say that an n-verte...   \n",
       "1467   \\n  For positive reals η and σ, we say that A\\...   \n",
       "1468   \\n  For positive reals η and σ, we say that A\\...   \n",
       "1478   \\nLet G be a 2-edge-colored multigraph. We say...   \n",
       "1507   [<cit.>]\\n\\nLet G be a finite permutation grou...   \n",
       "1657   \\n\\n\\n   B_MATH_TERM  Let G be a unlooped simp...   \n",
       "1658   \\n  A delta-matroid is binary if and only if i...   \n",
       "2295   \\nLet B_MATH_TERM(G)be all orientations ofGand...   \n",
       "2401   [<cit.>]\\nSuppose that B_MATH_TERM is a decrea...   \n",
       "2402   \\nSuppose that B_MATH_TERM is a decreasing seq...   \n",
       "2707    <cit.>\\nAn object X ∈^b (Q) is a B_MATH_TERM ...   \n",
       "3307   [ Tangency conditions described by pairs of\\n ...   \n",
       "3600   [Favaron <cit.>]\\nA graph G with vertex-connec...   \n",
       "3601   [Favaron  <cit.>]\\n\\n    Let G be a 2-connecte...   \n",
       "3746   \\nB_MATH_TERMada <cit.>) Let G be a claw-o-hea...   \n",
       "4053   \\n\\nA collection C of arcs and essential loops...   \n",
       "4778   \\n\\nLet k be a fixed positive integer, and let...   \n",
       "4948   \\nSuppose 𝔓=(Σ, R, C) is a Parikh rewriting sy...   \n",
       "6397   [Balanced tracking decomposition – odd case]\\n...   \n",
       "6398   [Balanced tracking decomposition – even case]\\...   \n",
       "6497    \\nLet G and H be graphs on which a combinator...   \n",
       "6566   \\n       For a family of irreducible intervals...   \n",
       "6567   \\n     \\n       For a \\n       family of irred...   \n",
       "6568   \\n     Let B_MATH_TERM be the family of proper...   \n",
       "6685    \\n\\n\\n  * Let D be a digraph, and let 𝒫={P_1,...   \n",
       "7161   \\nFor all 0 <  < 1 there exists a constant C>0...   \n",
       "7472   \\n  Let 𝒩 be a set of matroids, let M be a mat...   \n",
       "7750   \\n\\nThe values of a_3^s(n), a_3^s(n), p_3^s(n)...   \n",
       "7913   \\nLet 𝔏 be a map from graphs to subsets of _≥ ...   \n",
       "8035    \\nAssume that k, k_2, Δ are such that:\\n\\n\\n ...   \n",
       "8110   \\n\\tНазовем B_MATH_TERM пары подмножеств (A, B...   \n",
       "8530   \\nB_MATH_TERM Let s≥ 2 and n≥ 2 be integers. I...   \n",
       "9477   \\n Компоненты h-вектора многогранника GZ(1  2^...   \n",
       "9925   \\n \\tFor any non-bipartite graphs H_i, i∈[k], ...   \n",
       "12726  [<cit.>]\\nThe sequence  B_MATH_TERM is biparti...   \n",
       "12727  \\nThe sequence  B_MATH_TERM  is bipartite grap...   \n",
       "13675  \\nLet Q be a quiver with vertices V,  associat...   \n",
       "15601  \\nLet (  P,γ) be a labeled poset. A\\nB_MATH_TE...   \n",
       "17087  The polar complex of a neural code  is the sim...   \n",
       "\n",
       "                                             labeled_def  \n",
       "255    O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "542    O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "647    O O O O O O O O O O O O O O O O O O O B_MATH_T...  \n",
       "1463   O O O O O O O O O O O O O O B_MATH_TERM O O O ...  \n",
       "1464   O O O O O O O O O O O O O O B_MATH_TERM O O O ...  \n",
       "1465   O O O O O O O O O O O O O B_MATH_TERM O O O O ...  \n",
       "1467   O O O O O O O O O O O B_MATH_TERM O O O O O O ...  \n",
       "1468   O O O O O O O O O O O B_MATH_TERM O O O O O O ...  \n",
       "1478   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "1507   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "1657   B_MATH_TERM O O O O O O O O O O O O O O O O O ...  \n",
       "1658   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "2295                 O O O O O O O O O O O O O O O O O O  \n",
       "2401   O O O B_MATH_TERM O O O O O O O O O O O O O O ...  \n",
       "2402   O O B_MATH_TERM O O O O O O O O O O O O O O O ...  \n",
       "2707   O O O O O O O O B_MATH_TERM O O O O O O O O O ...  \n",
       "3307   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "3600   O O O O O O O O O O O O O O O O O O O O O O B_...  \n",
       "3601   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "3746   O O O O O O O O O B_MATH_TERM O O O O O O B_MA...  \n",
       "4053   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "4778   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "4948   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "6397   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "6398   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "6497   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "6566   O O O O O O O O O B_MATH_TERM O O O O O O O O ...  \n",
       "6567   O O O O O O O O O B_MATH_TERM O O O O O O O O ...  \n",
       "6568               O B_MATH_TERM O O O O O O O O O O O O  \n",
       "6685   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "7161   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "7472   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "7750   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "7913   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "8035   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "8110           O B_MATH_TERM O O O O O O O O O O O O O O  \n",
       "8530   B_MATH_TERM O O O O O O O O O O O O O O O O O ...  \n",
       "9477   O O O O O O O O O O O O O O B_MATH_TERM O O O ...  \n",
       "9925   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "12726        O O O B_MATH_TERM O O O O O O O O O O O O O  \n",
       "12727        O O B_MATH_TERM O O O O O O O O O O O O O O  \n",
       "13675  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "15601  O O O O O O O O O O B_MATH_TERM O O O O O O O ...  \n",
       "17087  O O O O O O O O O O O B_MATH_TERM O O O O O O ...  "
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import string\n",
    "df_clean[df_clean['plain_text_term'].apply(lambda x: all(c not in string.ascii_letters for c in x))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "ea165839-2091-4740-918a-5cb72d94e745",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean = df_clean[~df_clean['plain_text_term'].apply(lambda x: all(c not in string.ascii_letters for c in x))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "af437f51-eeab-4c29-8657-956de5e10e31",
   "metadata": {},
   "outputs": [],
   "source": [
    "# ex*, i.e., <cite>, i;ii"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "f2529f92-b221-4824-a5bf-c8b16e860b48",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>term</th>\n",
       "      <th>def</th>\n",
       "      <th>file_name</th>\n",
       "      <th>extraction_rule</th>\n",
       "      <th>plain_text_def</th>\n",
       "      <th>plain_text_term</th>\n",
       "      <th>masked_plain_text_def</th>\n",
       "      <th>labeled_def</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>3235</th>\n",
       "      <td>i;ii</td>\n",
       "      <td>\\textbf{Laplacian test for fractals~\\cite{Kiga...</td>\n",
       "      <td>/home/shufan/que_tex/Optimization_algorithm_on...</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>Laplacian test for fractals &lt;cit.&gt;\\n\\n\\t\\nGive...</td>\n",
       "      <td>i;ii</td>\n",
       "      <td>Laplacian test for fractals &lt;cit.&gt;\\n\\n\\t\\nGive...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O B_MATH_TER...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3238</th>\n",
       "      <td>i;ii</td>\n",
       "      <td>\\n\\t  \\n \\n\\noindent We define:\\n\\n\\begin{item...</td>\n",
       "      <td>/home/shufan/que_tex/Optimization_algorithm_on...</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\n\\t  \\n \\nWe define:\\n\\n  \\n\\t\\n\\t\\n\\t\\n   i ...</td>\n",
       "      <td>i;ii</td>\n",
       "      <td>\\n\\t  \\n \\nWe define:\\n\\n  \\n\\t\\n\\t\\n\\t\\n   B_...</td>\n",
       "      <td>O O B_MATH_TERM O O O O O O O O O O B_MATH_TER...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3241</th>\n",
       "      <td>i;ii</td>\n",
       "      <td>{\\textbf{Extrema }}\\\\\\n\\t\\n\\noindent Given a c...</td>\n",
       "      <td>/home/shufan/que_tex/Optimization_algorithm_on...</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>Extrema \\n\\n\\t\\nGiven a continuous function u ...</td>\n",
       "      <td>i;ii</td>\n",
       "      <td>Extrema \\n\\n\\t\\nGiven a continuous function u ...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O B_MA...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8839</th>\n",
       "      <td>c;c;c;c;c;c</td>\n",
       "      <td>\\label{def:A}\\nLet $E$ be a heap and let \\n\\b...</td>\n",
       "      <td>/home/shufan/que_tex/ArXThesis.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nLet E be a heap and let \\n\\nc = {α_1, α_2, ...</td>\n",
       "      <td>c;c;c;c;c;c</td>\n",
       "      <td>\\nLet E be a heap and let \\n\\nB_MATH_TERM = {...</td>\n",
       "      <td>O O O O O O O B_MATH_TERM O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9113</th>\n",
       "      <td>i;i</td>\n",
       "      <td>\\nLet $P_m, P_n$ be a path of order $m, n \\ge ...</td>\n",
       "      <td>/home/shufan/que_tex/1402.0615.tex</td>\n",
       "      <td>theorem + \\textit{}</td>\n",
       "      <td>\\nLet P_m, P_n be a path of order m, n ≥ 2. Th...</td>\n",
       "      <td>i;i</td>\n",
       "      <td>\\nLet P_m, P_n be a path of order m, n ≥ 2. Th...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9114</th>\n",
       "      <td>i;i;i;i;i</td>\n",
       "      <td>\\nLet $C_m$ be a cycle of order $m \\ge3$ and $...</td>\n",
       "      <td>/home/shufan/que_tex/1402.0615.tex</td>\n",
       "      <td>theorem + \\textit{}</td>\n",
       "      <td>\\nLet C_m be a cycle of order m ≥3 and P_n be ...</td>\n",
       "      <td>i;i;i;i;i</td>\n",
       "      <td>\\nLet C_m be a cycle of order m ≥3 and P_n be ...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9115</th>\n",
       "      <td>i;i</td>\n",
       "      <td>\\nLet $S_m$ be the star graph of order $m \\ge ...</td>\n",
       "      <td>/home/shufan/que_tex/1402.0615.tex</td>\n",
       "      <td>theorem + \\textit{}</td>\n",
       "      <td>\\nLet S_m be the star graph of order m ≥ 2 and...</td>\n",
       "      <td>i;i</td>\n",
       "      <td>\\nLet S_m be the star graph of order m ≥ 2 and...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9116</th>\n",
       "      <td>i;i;i;i</td>\n",
       "      <td>\\nLet $K_m$ be a\\ncomplete graph of order $m \\...</td>\n",
       "      <td>/home/shufan/que_tex/1402.0615.tex</td>\n",
       "      <td>theorem + \\textit{}</td>\n",
       "      <td>\\nLet K_m be a\\ncomplete graph of order m ≥ 2 ...</td>\n",
       "      <td>i;i;i;i</td>\n",
       "      <td>\\nLet K_m be a\\ncomplete graph of order m ≥ 2 ...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9117</th>\n",
       "      <td>i;i</td>\n",
       "      <td>\\nLet $W_m$ be a wheel graph of\\norder $m \\ge ...</td>\n",
       "      <td>/home/shufan/que_tex/1402.0615.tex</td>\n",
       "      <td>theorem + \\textit{}</td>\n",
       "      <td>\\nLet W_m be a wheel graph of\\norder m ≥ 3 and...</td>\n",
       "      <td>i;i</td>\n",
       "      <td>\\nLet W_m be a wheel graph of\\norder m ≥ 3 and...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9118</th>\n",
       "      <td>i;i;i;i;i;i;i;i;i;i;i</td>\n",
       "      <td>\\n Let $C_n, C_m$ be a cycle of order $n, m \\g...</td>\n",
       "      <td>/home/shufan/que_tex/1402.0615.tex</td>\n",
       "      <td>theorem + \\textit{}</td>\n",
       "      <td>\\n Let C_n, C_m be a cycle of order n, m ≥ 3. ...</td>\n",
       "      <td>i;i;i;i;i;i;i;i;i;i;i</td>\n",
       "      <td>\\n Let C_n, C_m be a cycle of order n, m ≥ 3. ...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9937</th>\n",
       "      <td>i;ii</td>\n",
       "      <td>\\nThe prescribed sequences in the J-fraction ...</td>\n",
       "      <td>/home/shufan/que_tex/schmidt14.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nThe prescribed sequences in the J-fraction ...</td>\n",
       "      <td>i;ii</td>\n",
       "      <td>\\nThe prescribed sequences in the J-fraction ...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O B_MATH_TERM ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10929</th>\n",
       "      <td>i;ii</td>\n",
       "      <td>[partial unimodality for cubical polytopes]\\la...</td>\n",
       "      <td>/home/shufan/que_tex/1501.00430.tex</td>\n",
       "      <td>theorem + \\textit{}</td>\n",
       "      <td>[partial unimodality for cubical polytopes]\\nL...</td>\n",
       "      <td>i;ii</td>\n",
       "      <td>[partial unimodality for cubical polytopes]\\nL...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O B_MATH_TERM ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13390</th>\n",
       "      <td>l;l;l</td>\n",
       "      <td>\\nFor $n\\geq 1$ and $0\\leq k\\leq n$, we have\\n...</td>\n",
       "      <td>/home/shufan/que_tex/1106.5781.tex</td>\n",
       "      <td>theorem + \\textit{}</td>\n",
       "      <td>\\nFor n≥ 1 and 0≤ k≤ n, we have\\n\\n    R_n+1,k...</td>\n",
       "      <td>l;l;l</td>\n",
       "      <td>\\nFor n≥ 1 and 0≤ k≤ n, we have\\n\\n    R_n+1,k...</td>\n",
       "      <td>O O O O O O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15816</th>\n",
       "      <td>i;ii</td>\n",
       "      <td>\\textbf{Spline functions on~${\\cal D}\\left (\\G...</td>\n",
       "      <td>/home/shufan/que_tex/W.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>Spline functions on D (Γ_ W_m), m ∈ ^⋆\\n\\n\\t\\n...</td>\n",
       "      <td>i;ii</td>\n",
       "      <td>Spline functions on D (Γ_ W_m), m ∈ ^⋆\\n\\n\\t\\n...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16713</th>\n",
       "      <td>i;i</td>\n",
       "      <td>\\nLet $G=(V,E)$ be a graph and $W$ a vertex su...</td>\n",
       "      <td>/home/shufan/que_tex/1602.08250.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nLet G=(V,E) be a graph and W a vertex subset...</td>\n",
       "      <td>i;i</td>\n",
       "      <td>\\nLet G=(V,E) be a graph and W a vertex subset...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17700</th>\n",
       "      <td>i;ii</td>\n",
       "      <td>\\n\\label{thm2413}\\nAssume $\\tau \\in S_k$ and ...</td>\n",
       "      <td>/home/shufan/que_tex/ejc-June-20.tex</td>\n",
       "      <td>theorem + \\textit{}</td>\n",
       "      <td>\\n\\nAssume τ∈ S_k and satisfies at least one ...</td>\n",
       "      <td>i;ii</td>\n",
       "      <td>\\n\\nAssume τ∈ S_k and satisfies at least one ...</td>\n",
       "      <td>O O O O O O O O O O O O O B_MATH_TERM O O O O ...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                        term  \\\n",
       "3235                    i;ii   \n",
       "3238                    i;ii   \n",
       "3241                    i;ii   \n",
       "8839             c;c;c;c;c;c   \n",
       "9113                     i;i   \n",
       "9114               i;i;i;i;i   \n",
       "9115                     i;i   \n",
       "9116                 i;i;i;i   \n",
       "9117                     i;i   \n",
       "9118   i;i;i;i;i;i;i;i;i;i;i   \n",
       "9937                    i;ii   \n",
       "10929                   i;ii   \n",
       "13390                  l;l;l   \n",
       "15816                   i;ii   \n",
       "16713                    i;i   \n",
       "17700                   i;ii   \n",
       "\n",
       "                                                     def  \\\n",
       "3235   \\textbf{Laplacian test for fractals~\\cite{Kiga...   \n",
       "3238   \\n\\t  \\n \\n\\noindent We define:\\n\\n\\begin{item...   \n",
       "3241   {\\textbf{Extrema }}\\\\\\n\\t\\n\\noindent Given a c...   \n",
       "8839    \\label{def:A}\\nLet $E$ be a heap and let \\n\\b...   \n",
       "9113   \\nLet $P_m, P_n$ be a path of order $m, n \\ge ...   \n",
       "9114   \\nLet $C_m$ be a cycle of order $m \\ge3$ and $...   \n",
       "9115   \\nLet $S_m$ be the star graph of order $m \\ge ...   \n",
       "9116   \\nLet $K_m$ be a\\ncomplete graph of order $m \\...   \n",
       "9117   \\nLet $W_m$ be a wheel graph of\\norder $m \\ge ...   \n",
       "9118   \\n Let $C_n, C_m$ be a cycle of order $n, m \\g...   \n",
       "9937    \\nThe prescribed sequences in the J-fraction ...   \n",
       "10929  [partial unimodality for cubical polytopes]\\la...   \n",
       "13390  \\nFor $n\\geq 1$ and $0\\leq k\\leq n$, we have\\n...   \n",
       "15816  \\textbf{Spline functions on~${\\cal D}\\left (\\G...   \n",
       "16713  \\nLet $G=(V,E)$ be a graph and $W$ a vertex su...   \n",
       "17700   \\n\\label{thm2413}\\nAssume $\\tau \\in S_k$ and ...   \n",
       "\n",
       "                                               file_name  \\\n",
       "3235   /home/shufan/que_tex/Optimization_algorithm_on...   \n",
       "3238   /home/shufan/que_tex/Optimization_algorithm_on...   \n",
       "3241   /home/shufan/que_tex/Optimization_algorithm_on...   \n",
       "8839                  /home/shufan/que_tex/ArXThesis.tex   \n",
       "9113                  /home/shufan/que_tex/1402.0615.tex   \n",
       "9114                  /home/shufan/que_tex/1402.0615.tex   \n",
       "9115                  /home/shufan/que_tex/1402.0615.tex   \n",
       "9116                  /home/shufan/que_tex/1402.0615.tex   \n",
       "9117                  /home/shufan/que_tex/1402.0615.tex   \n",
       "9118                  /home/shufan/que_tex/1402.0615.tex   \n",
       "9937                  /home/shufan/que_tex/schmidt14.tex   \n",
       "10929                /home/shufan/que_tex/1501.00430.tex   \n",
       "13390                 /home/shufan/que_tex/1106.5781.tex   \n",
       "15816                         /home/shufan/que_tex/W.tex   \n",
       "16713                /home/shufan/que_tex/1602.08250.tex   \n",
       "17700               /home/shufan/que_tex/ejc-June-20.tex   \n",
       "\n",
       "            extraction_rule  \\\n",
       "3235      theorem + \\emph{}   \n",
       "3238   definition + \\emph{}   \n",
       "3241   definition + \\emph{}   \n",
       "8839   definition + \\emph{}   \n",
       "9113    theorem + \\textit{}   \n",
       "9114    theorem + \\textit{}   \n",
       "9115    theorem + \\textit{}   \n",
       "9116    theorem + \\textit{}   \n",
       "9117    theorem + \\textit{}   \n",
       "9118    theorem + \\textit{}   \n",
       "9937   definition + \\emph{}   \n",
       "10929   theorem + \\textit{}   \n",
       "13390   theorem + \\textit{}   \n",
       "15816  definition + \\emph{}   \n",
       "16713  definition + \\emph{}   \n",
       "17700   theorem + \\textit{}   \n",
       "\n",
       "                                          plain_text_def  \\\n",
       "3235   Laplacian test for fractals <cit.>\\n\\n\\t\\nGive...   \n",
       "3238   \\n\\t  \\n \\nWe define:\\n\\n  \\n\\t\\n\\t\\n\\t\\n   i ...   \n",
       "3241   Extrema \\n\\n\\t\\nGiven a continuous function u ...   \n",
       "8839    \\nLet E be a heap and let \\n\\nc = {α_1, α_2, ...   \n",
       "9113   \\nLet P_m, P_n be a path of order m, n ≥ 2. Th...   \n",
       "9114   \\nLet C_m be a cycle of order m ≥3 and P_n be ...   \n",
       "9115   \\nLet S_m be the star graph of order m ≥ 2 and...   \n",
       "9116   \\nLet K_m be a\\ncomplete graph of order m ≥ 2 ...   \n",
       "9117   \\nLet W_m be a wheel graph of\\norder m ≥ 3 and...   \n",
       "9118   \\n Let C_n, C_m be a cycle of order n, m ≥ 3. ...   \n",
       "9937    \\nThe prescribed sequences in the J-fraction ...   \n",
       "10929  [partial unimodality for cubical polytopes]\\nL...   \n",
       "13390  \\nFor n≥ 1 and 0≤ k≤ n, we have\\n\\n    R_n+1,k...   \n",
       "15816  Spline functions on D (Γ_ W_m), m ∈ ^⋆\\n\\n\\t\\n...   \n",
       "16713  \\nLet G=(V,E) be a graph and W a vertex subset...   \n",
       "17700   \\n\\nAssume τ∈ S_k and satisfies at least one ...   \n",
       "\n",
       "             plain_text_term  \\\n",
       "3235                    i;ii   \n",
       "3238                    i;ii   \n",
       "3241                    i;ii   \n",
       "8839             c;c;c;c;c;c   \n",
       "9113                     i;i   \n",
       "9114               i;i;i;i;i   \n",
       "9115                     i;i   \n",
       "9116                 i;i;i;i   \n",
       "9117                     i;i   \n",
       "9118   i;i;i;i;i;i;i;i;i;i;i   \n",
       "9937                    i;ii   \n",
       "10929                   i;ii   \n",
       "13390                  l;l;l   \n",
       "15816                   i;ii   \n",
       "16713                    i;i   \n",
       "17700                   i;ii   \n",
       "\n",
       "                                   masked_plain_text_def  \\\n",
       "3235   Laplacian test for fractals <cit.>\\n\\n\\t\\nGive...   \n",
       "3238   \\n\\t  \\n \\nWe define:\\n\\n  \\n\\t\\n\\t\\n\\t\\n   B_...   \n",
       "3241   Extrema \\n\\n\\t\\nGiven a continuous function u ...   \n",
       "8839    \\nLet E be a heap and let \\n\\nB_MATH_TERM = {...   \n",
       "9113   \\nLet P_m, P_n be a path of order m, n ≥ 2. Th...   \n",
       "9114   \\nLet C_m be a cycle of order m ≥3 and P_n be ...   \n",
       "9115   \\nLet S_m be the star graph of order m ≥ 2 and...   \n",
       "9116   \\nLet K_m be a\\ncomplete graph of order m ≥ 2 ...   \n",
       "9117   \\nLet W_m be a wheel graph of\\norder m ≥ 3 and...   \n",
       "9118   \\n Let C_n, C_m be a cycle of order n, m ≥ 3. ...   \n",
       "9937    \\nThe prescribed sequences in the J-fraction ...   \n",
       "10929  [partial unimodality for cubical polytopes]\\nL...   \n",
       "13390  \\nFor n≥ 1 and 0≤ k≤ n, we have\\n\\n    R_n+1,k...   \n",
       "15816  Spline functions on D (Γ_ W_m), m ∈ ^⋆\\n\\n\\t\\n...   \n",
       "16713  \\nLet G=(V,E) be a graph and W a vertex subset...   \n",
       "17700   \\n\\nAssume τ∈ S_k and satisfies at least one ...   \n",
       "\n",
       "                                             labeled_def  \n",
       "3235   O O O O O O O O O O O O O O O O O O B_MATH_TER...  \n",
       "3238   O O B_MATH_TERM O O O O O O O O O O B_MATH_TER...  \n",
       "3241   O O O O O O O O O O O O O O O O O O O O O B_MA...  \n",
       "8839   O O O O O O O B_MATH_TERM O O O O O O O O O O ...  \n",
       "9113   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "9114   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "9115   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "9116   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "9117   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "9118   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "9937   O O O O O O O O O O O O O O O O O B_MATH_TERM ...  \n",
       "10929  O O O O O O O O O O O O O O O O O B_MATH_TERM ...  \n",
       "13390                          O O O O O O O O O O O O O  \n",
       "15816  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "16713  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "17700  O O O O O O O O O O O O O B_MATH_TERM O O O O ...  "
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_clean[ df_clean['plain_text_term'].str.match(r'^\\s*([ivxlcd]+\\s*([,;]\\s*[ivxlcd]+\\s*)*)$')] # remove m to not exlude 'mild'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "f5c44cbb-6b9b-438d-bcd6-652f9db62b77",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean = df_clean[~df_clean['plain_text_term'].str.match(r'^\\s*([ivxlcd]+\\s*([,;]\\s*[ivxlcd]+\\s*)*)$')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "d751dfff-97e4-4fd7-991a-fe974957cded",
   "metadata": {},
   "outputs": [
    {
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       "      <th>labeled_def</th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>5767</th>\n",
       "      <td>i.e.;i.e.</td>\n",
       "      <td>[\\cite{MihalceaAdvances}]\\label{T:OneBoxPlusPi...</td>\n",
       "      <td>/home/shufan/que_tex/arXivPost3_24_14.tex</td>\n",
       "      <td>theorem + \\textit{}</td>\n",
       "      <td>[&lt;cit.&gt;]\\nLet Λ = [t_1, …, t_n].  Suppose that...</td>\n",
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       "      <th>7360</th>\n",
       "      <td>i.e.</td>\n",
       "      <td>\\n$S(n,3)$ has Lex nested solutions for $EIP$\\...</td>\n",
       "      <td>/home/shufan/que_tex/eiponsn3a.tex</td>\n",
       "      <td>theorem + \\textit{}</td>\n",
       "      <td>\\nS(n,3) has Lex nested solutions for EIP\\n\\n\\...</td>\n",
       "      <td>i.e.</td>\n",
       "      <td>\\nS(n,3) has Lex nested solutions for EIP\\n\\n\\...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
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       "    <tr>\n",
       "      <th>10816</th>\n",
       "      <td>i.e.</td>\n",
       "      <td>\\label{Thm:DLW}\\n\\tConsider the following syst...</td>\n",
       "      <td>/home/shufan/que_tex/ClassesNonCloses.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n\\tConsider the following system:\\n\\t\\n    &lt;r...</td>\n",
       "      <td>i.e.</td>\n",
       "      <td>\\n\\tConsider the following system:\\n\\t\\n    &lt;r...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
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       "            term                                                def  \\\n",
       "5767   i.e.;i.e.  [\\cite{MihalceaAdvances}]\\label{T:OneBoxPlusPi...   \n",
       "7360       i.e.   \\n$S(n,3)$ has Lex nested solutions for $EIP$\\...   \n",
       "10816      i.e.   \\label{Thm:DLW}\\n\\tConsider the following syst...   \n",
       "\n",
       "                                       file_name      extraction_rule  \\\n",
       "5767   /home/shufan/que_tex/arXivPost3_24_14.tex  theorem + \\textit{}   \n",
       "7360          /home/shufan/que_tex/eiponsn3a.tex  theorem + \\textit{}   \n",
       "10816  /home/shufan/que_tex/ClassesNonCloses.tex    theorem + \\emph{}   \n",
       "\n",
       "                                          plain_text_def plain_text_term  \\\n",
       "5767   [<cit.>]\\nLet Λ = [t_1, …, t_n].  Suppose that...       i.e.;i.e.   \n",
       "7360   \\nS(n,3) has Lex nested solutions for EIP\\n\\n\\...           i.e.    \n",
       "10816  \\n\\tConsider the following system:\\n\\t\\n    <r...           i.e.    \n",
       "\n",
       "                                   masked_plain_text_def  \\\n",
       "5767   [<cit.>]\\nLet Λ = [t_1, …, t_n].  Suppose that...   \n",
       "7360   \\nS(n,3) has Lex nested solutions for EIP\\n\\n\\...   \n",
       "10816  \\n\\tConsider the following system:\\n\\t\\n    <r...   \n",
       "\n",
       "                                             labeled_def  \n",
       "5767   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "7360   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "10816  O O O O O O O O O O O O O O O O O O O O O O O ...  "
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_clean[ df_clean['plain_text_term'].str.match(r'^\\s*([i.e]+\\s*([,;]\\s*[i.e]+\\s*)*)$')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "d1281edf-bdab-4001-ae38-15bb3b19c422",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean = df_clean[~df_clean['plain_text_term'].str.match(r'^\\s*([i.e]+\\s*([,;]\\s*[i.e]+\\s*)*)$')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "a7ca1715-7546-4a62-9c35-ef829d543e89",
   "metadata": {},
   "outputs": [
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       "      <th>1856</th>\n",
       "      <td>ex</td>\n",
       "      <td>\\cite{erdHos1966}\\label{p+1 chromatic}\\nIf $\\m...</td>\n",
       "      <td>/home/shufan/que_tex/1903.10319.tex</td>\n",
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       "      <th>11684</th>\n",
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       "      <td>/home/shufan/que_tex/0810.3670.tex</td>\n",
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       "      <th>11685</th>\n",
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       "      <td>ex;ex</td>\n",
       "      <td>\\nIf P is  chosen uniformly at random from _0,...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O</td>\n",
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      ],
      "text/plain": [
       "           term                                                def  \\\n",
       "1856         ex  \\cite{erdHos1966}\\label{p+1 chromatic}\\nIf $\\m...   \n",
       "11684  ex;ex;ex  \\n  \\label{thm:SMain}\\nIf $P$ is  chosen unifo...   \n",
       "11685     ex;ex  \\label{thm:convavg}\\nIf $P$ is  chosen uniform...   \n",
       "\n",
       "                                 file_name    extraction_rule  \\\n",
       "1856   /home/shufan/que_tex/1903.10319.tex  theorem + \\emph{}   \n",
       "11684   /home/shufan/que_tex/0810.3670.tex  theorem + \\emph{}   \n",
       "11685   /home/shufan/que_tex/0810.3670.tex  theorem + \\emph{}   \n",
       "\n",
       "                                          plain_text_def plain_text_term  \\\n",
       "1856   <cit.>\\nIf ℒ is a family of graphs with subchr...              ex   \n",
       "11684  \\n  \\nIf P is  chosen uniformly at random from...        ex;ex;ex   \n",
       "11685  \\nIf P is  chosen uniformly at random from _0,...           ex;ex   \n",
       "\n",
       "                                   masked_plain_text_def  \\\n",
       "1856   <cit.>\\nIf ℒ is a family of graphs with subchr...   \n",
       "11684  \\n  \\nIf P is  chosen uniformly at random from...   \n",
       "11685  \\nIf P is  chosen uniformly at random from _0,...   \n",
       "\n",
       "                                             labeled_def  \n",
       "1856                       O O O O O O O O O O O O O O O  \n",
       "11684  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "11685        O O O O O O O O O O O O O O O O O O O O O O  "
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_clean[ df_clean['plain_text_term'].str.match(r'^\\s*([ex.]+\\s*([,;]\\s*[ex.]+\\s*)*)$')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "3c00ec92-cb69-40c2-bef1-a83c7d34dfb1",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean = df_clean[~df_clean['plain_text_term'].str.match(r'^\\s*([ex.]+\\s*([,;]\\s*[ex.]+\\s*)*)$')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "88a779d7-d6b6-4c6f-b5fe-6e3db561666a",
   "metadata": {},
   "outputs": [
    {
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       "      <td>\\label{THM:mod 2}\\nFor all $n\\geq0$,\\n\\begin{a...</td>\n",
       "      <td>/home/shufan/que_tex/1805.06575.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nFor all n≥0,\\n\\n    M^*(0,2,n)    &gt;M^*(1,2,n...</td>\n",
       "      <td>if;if</td>\n",
       "      <td>\\nFor all n≥0,\\n\\n    M^*(0,2,n)    &gt;M^*(1,2,n...</td>\n",
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       "      <th>4698</th>\n",
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       "      <td>\\label{THM:mod 3}\\nFor all $n\\geq0$,\\n\\begin{a...</td>\n",
       "      <td>/home/shufan/que_tex/1805.06575.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nFor all n≥0,\\n\\n    M^*(0,3,n)   &gt;M^*(1,3,n)...</td>\n",
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       "      <td>\\nFor all n≥0,\\n\\n    M^*(0,3,n)   &gt;M^*(1,3,n)...</td>\n",
       "      <td>O O O O O B_MATH_TERM O O O O O B_MATH_TERM O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4699</th>\n",
       "      <td>if;if;if</td>\n",
       "      <td>\\label{th:main-asy}\\nFor $n\\ge 1$,\\n\\begin{equ...</td>\n",
       "      <td>/home/shufan/que_tex/1805.06575.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nFor n≥ 1,\\n\\n    M^*(0,3,n)-M^*(1,3,n)=c(n) ...</td>\n",
       "      <td>if;if;if</td>\n",
       "      <td>\\nFor n≥ 1,\\n\\n    M^*(0,3,n)-M^*(1,3,n)=c(n) ...</td>\n",
       "      <td>O O O O O O O B_MATH_TERM O O O O B_MATH_TERM ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4700</th>\n",
       "      <td>if;if</td>\n",
       "      <td>\\label{THM:mod 4}\\nFor all $n\\geq0$,\\n\\begin{a...</td>\n",
       "      <td>/home/shufan/que_tex/1805.06575.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nFor all n≥0,\\n\\n    M^*(0,4,n)   &gt;M^*(2,4,n)...</td>\n",
       "      <td>if;if</td>\n",
       "      <td>\\nFor all n≥0,\\n\\n    M^*(0,4,n)   &gt;M^*(2,4,n)...</td>\n",
       "      <td>O O O O O B_MATH_TERM O O O O O B_MATH_TERM O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4741</th>\n",
       "      <td>if;or;if</td>\n",
       "      <td>\\n\\label{Th8}\\nLet $ T $ be a tree with $ c(T)...</td>\n",
       "      <td>/home/shufan/que_tex/Inertia.tex</td>\n",
       "      <td>theorem + \\textit{}</td>\n",
       "      <td>\\n\\nLet T be a tree with c(T)≥ 1.\\nThen\\n\\n   ...</td>\n",
       "      <td>if;or;if</td>\n",
       "      <td>\\n\\nLet T be a tree with c(T)≥ 1.\\nThen\\n\\n   ...</td>\n",
       "      <td>O O O O O O O O O O O B_MATH_TERM O B_MATH_TER...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4990</th>\n",
       "      <td>iff</td>\n",
       "      <td>\\n\\label{[x]def} \\cite{ESS}, 3.2. Let $(X,r)$ ...</td>\n",
       "      <td>/home/shufan/que_tex/CYBE30507JSC.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\n &lt;cit.&gt;, 3.2. Let (X,r) be a nondegenerate\\n...</td>\n",
       "      <td>iff</td>\n",
       "      <td>\\n &lt;cit.&gt;, 3.2. Let (X,r) be a nondegenerate\\n...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O B_MA...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4996</th>\n",
       "      <td>iff</td>\n",
       "      <td>By $\\Gamma(x)$ we denote the\\nsubgraph of (th...</td>\n",
       "      <td>/home/shufan/que_tex/CYBE30507JSC.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>By Γ(x) we denote the\\nsubgraph of (the\\ncomp...</td>\n",
       "      <td>iff</td>\n",
       "      <td>By Γ(x) we denote the\\nsubgraph of (the\\ncomp...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5656</th>\n",
       "      <td>if ;if ;if</td>\n",
       "      <td>\\label{Thm:mod 5}\\nFor all $n\\geq0$,\\n\\begin{a...</td>\n",
       "      <td>/home/shufan/que_tex/1706.08223.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nFor all n≥0,\\n\\n    w_t(5n+3)≡ w_t(5n+4)≡ 05...</td>\n",
       "      <td>if ;if ;if</td>\n",
       "      <td>\\nFor all n≥0,\\n\\n    w_t(5n+3)≡ w_t(5n+4)≡ 05...</td>\n",
       "      <td>O O O O O O B_MATH_TERM O O O O B_MATH_TERM O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5657</th>\n",
       "      <td>if ;if ;if</td>\n",
       "      <td>\\label{weighted analog thm }\\nFor all $n\\geq0$...</td>\n",
       "      <td>/home/shufan/que_tex/1706.08223.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nFor all n≥0,\\n\\n    c_t(5n+3)= c_t(5n+4)= 0,...</td>\n",
       "      <td>if ;if ;if</td>\n",
       "      <td>\\nFor all n≥0,\\n\\n    c_t(5n+3)= c_t(5n+4)= 0,...</td>\n",
       "      <td>O O O O O O B_MATH_TERM O O O O B_MATH_TERM O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5688</th>\n",
       "      <td>for;for;for</td>\n",
       "      <td>\\label{thm:alternate thm}\\nFor $n\\geq0$,\\n\\beg...</td>\n",
       "      <td>/home/shufan/que_tex/1705.10067.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nFor n≥0,\\n\\n    M_k(0,2,2n)    &gt;M_k(1,2,2n),...</td>\n",
       "      <td>for;for;for</td>\n",
       "      <td>\\nFor n≥0,\\n\\n    M_k(0,2,2n)    &gt;M_k(1,2,2n),...</td>\n",
       "      <td>O O O O B_MATH_TERM O O O B_MATH_TERM O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5689</th>\n",
       "      <td>for ;for</td>\n",
       "      <td>\\label{Kane thm}\\nFor $n\\geq0$,\\n\\begin{align*...</td>\n",
       "      <td>/home/shufan/que_tex/1705.10067.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nFor n≥0,\\n\\n    M(0,3,3n)    &gt;M(1,3,3n),\\n  ...</td>\n",
       "      <td>for ;for</td>\n",
       "      <td>\\nFor n≥0,\\n\\n    M(0,3,3n)    &gt;M(1,3,3n),\\n  ...</td>\n",
       "      <td>O O O O O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5690</th>\n",
       "      <td>for</td>\n",
       "      <td>\\label{+--thm}\\nFor all $n\\geq0$,\\n\\begin{alig...</td>\n",
       "      <td>/home/shufan/que_tex/1705.10067.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nFor all n≥0,\\n\\n    M_2(0,3,3n)    &gt;M_2(1,3,...</td>\n",
       "      <td>for</td>\n",
       "      <td>\\nFor all n≥0,\\n\\n    M_2(0,3,3n)    &gt;M_2(1,3,...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O B_MA...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5691</th>\n",
       "      <td>for;for</td>\n",
       "      <td>[Theorem~3 in \\cite{AL}]\\nFor $n&gt;0$,\\n\\begin{a...</td>\n",
       "      <td>/home/shufan/que_tex/1705.10067.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>[Theorem 3 in &lt;cit.&gt;]\\nFor n&gt;0,\\n\\n    M(0,4,2...</td>\n",
       "      <td>for;for</td>\n",
       "      <td>[Theorem 3 in &lt;cit.&gt;]\\nFor n&gt;0,\\n\\n    M(0,4,2...</td>\n",
       "      <td>O O O O O O O O B_MATH_TERM O O O B_MATH_TERM ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5692</th>\n",
       "      <td>for;for</td>\n",
       "      <td>\\nFor $n&gt;0$,\\n\\begin{align}\\nM_{2}(0,4,4n) &amp;&gt;M...</td>\n",
       "      <td>/home/shufan/que_tex/1705.10067.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nFor n&gt;0,\\n\\n    M_2(0,4,4n)    &gt;M_2(2,4,4n)&gt;...</td>\n",
       "      <td>for;for</td>\n",
       "      <td>\\nFor n&gt;0,\\n\\n    M_2(0,4,4n)    &gt;M_2(2,4,4n)&gt;...</td>\n",
       "      <td>O O O O B_MATH_TERM O O O O O O O O O O O B_MA...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7290</th>\n",
       "      <td>or</td>\n",
       "      <td>\\n\\label{thm:uniformDegreeBound} \\n\\tGiven a $...</td>\n",
       "      <td>/home/shufan/que_tex/markovcomplexityDec19-for...</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n \\n\\tGiven a k-uniform hypergraph H, the tor...</td>\n",
       "      <td>or</td>\n",
       "      <td>\\n \\n\\tGiven a k-uniform hypergraph H, the tor...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7578</th>\n",
       "      <td>\\text o;\\text o</td>\n",
       "      <td>\\label{diameter}\\nWe have:\\n\\begin{enumerate}[...</td>\n",
       "      <td>/home/shufan/que_tex/Cone_poset_final.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nWe have:\\n\\n\\n  * ((d))=2d for every d∈,\\n\\n...</td>\n",
       "      <td>o;o</td>\n",
       "      <td>\\nWe have:\\n\\n\\n  * ((d))=2d for every d∈,\\n\\n...</td>\n",
       "      <td>O O O O O O O O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8855</th>\n",
       "      <td>or</td>\n",
       "      <td>\\n\\label{thm:cases}\\nSuppose $S_t$ is a parame...</td>\n",
       "      <td>/home/shufan/que_tex/ubiquitous_qps_full.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n\\nSuppose S_t is a parametric Presburger fam...</td>\n",
       "      <td>or</td>\n",
       "      <td>\\n\\nSuppose S_t is a parametric Presburger fam...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O B_MATH_TER...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11231</th>\n",
       "      <td>if</td>\n",
       "      <td>\\label{THM:mod 25}\\nFor all $n\\geq0$,\\n\\begin{...</td>\n",
       "      <td>/home/shufan/que_tex/1807.01890.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nFor all n≥0,\\n\\n    Δ_k(125n+99)    ≡025,   ...</td>\n",
       "      <td>if</td>\n",
       "      <td>\\nFor all n≥0,\\n\\n    Δ_k(125n+99)    ≡025,   ...</td>\n",
       "      <td>O O O O O B_MATH_TERM O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11352</th>\n",
       "      <td>or</td>\n",
       "      <td>\\label{thm:irreducible}\\nLet $\\lambda / \\lambd...</td>\n",
       "      <td>/home/shufan/que_tex/SL2Plethysms8+.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet λ / λ^⋆ be a proper skew partition.\\nThe...</td>\n",
       "      <td>or</td>\n",
       "      <td>\\nLet λ / λ^⋆ be a proper skew partition.\\nThe...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12602</th>\n",
       "      <td>if ;if</td>\n",
       "      <td>\\label{thm:main}\\nLet $A_{1}, A_{2}, \\cdots ,A...</td>\n",
       "      <td>/home/shufan/que_tex/t-matchings-final.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet A_1, A_2, ⋯ ,A_F be the first F = F_t -1...</td>\n",
       "      <td>if ;if</td>\n",
       "      <td>\\nLet A_1, A_2, ⋯ ,A_F be the first F = F_t -1...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14192</th>\n",
       "      <td>if ; if ; if ; if</td>\n",
       "      <td>\\n\\label{st:th5}\\nLet $\\Gamma$ be a simple con...</td>\n",
       "      <td>/home/shufan/que_tex/Stochastic_2016_04_25_AB.tex</td>\n",
       "      <td>theorem + \\textit{}</td>\n",
       "      <td>\\n\\nLet Γ be a simple connected graph of order...</td>\n",
       "      <td>if ; if ; if ; if</td>\n",
       "      <td>\\n\\nLet Γ be a simple connected graph of order...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14535</th>\n",
       "      <td>if ;if</td>\n",
       "      <td>\\n\\label{4n+1}\\nLet $D = \\{1,j,k\\}$ with $j=4n...</td>\n",
       "      <td>/home/shufan/que_tex/1611.03940.tex</td>\n",
       "      <td>theorem + \\textit{}</td>\n",
       "      <td>\\n\\nLet D = {1,j,k} with j=4n+1, k even, and k...</td>\n",
       "      <td>if ;if</td>\n",
       "      <td>\\n\\nLet D = {1,j,k} with j=4n+1, k even, and k...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16632</th>\n",
       "      <td>if</td>\n",
       "      <td>\\label{THM:mod 5}\\nFor all $n\\geq0$,\\n\\begin{a...</td>\n",
       "      <td>/home/shufan/que_tex/1709.02584.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nFor all n≥0,\\n\\n    Δ_k(25n+24)    ≡05,   if...</td>\n",
       "      <td>if</td>\n",
       "      <td>\\nFor all n≥0,\\n\\n    Δ_k(25n+24)    ≡05,    B...</td>\n",
       "      <td>O O O O O B_MATH_TERM O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16633</th>\n",
       "      <td>if</td>\n",
       "      <td>\\label{THM:mod 25}\\nFor all $n\\geq0$,\\n\\begin{...</td>\n",
       "      <td>/home/shufan/que_tex/1709.02584.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nFor all n≥0,\\n\\n    Δ_k(125n+99)    ≡025,   ...</td>\n",
       "      <td>if</td>\n",
       "      <td>\\nFor all n≥0,\\n\\n    Δ_k(125n+99)    ≡025,   ...</td>\n",
       "      <td>O O O O O B_MATH_TERM O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16634</th>\n",
       "      <td>if</td>\n",
       "      <td>\\label{THM:mod 7}\\nFor all $n\\geq0$,\\n\\begin{a...</td>\n",
       "      <td>/home/shufan/que_tex/1709.02584.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nFor all n≥0,\\n\\n    Δ_k(49n+s)≡07,   if   k≡...</td>\n",
       "      <td>if</td>\n",
       "      <td>\\nFor all n≥0,\\n\\n    Δ_k(49n+s)≡07,    B_MATH...</td>\n",
       "      <td>O O O O B_MATH_TERM O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16635</th>\n",
       "      <td>if</td>\n",
       "      <td>\\label{THM:mod 49}\\n\\begin{align}\\n\\Delta_{k}(...</td>\n",
       "      <td>/home/shufan/que_tex/1709.02584.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n\\n    Δ_k(343n+t)≡ 049,   if   k≡171343.\\n\\n...</td>\n",
       "      <td>if</td>\n",
       "      <td>\\n\\n    Δ_k(343n+t)≡ 049,    B_MATH_TERM   k≡1...</td>\n",
       "      <td>O O B_MATH_TERM O O O O O O</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                      term                                                def  \\\n",
       "4697                 if;if  \\label{THM:mod 2}\\nFor all $n\\geq0$,\\n\\begin{a...   \n",
       "4698                 if;if  \\label{THM:mod 3}\\nFor all $n\\geq0$,\\n\\begin{a...   \n",
       "4699              if;if;if  \\label{th:main-asy}\\nFor $n\\ge 1$,\\n\\begin{equ...   \n",
       "4700                 if;if  \\label{THM:mod 4}\\nFor all $n\\geq0$,\\n\\begin{a...   \n",
       "4741              if;or;if  \\n\\label{Th8}\\nLet $ T $ be a tree with $ c(T)...   \n",
       "4990                   iff  \\n\\label{[x]def} \\cite{ESS}, 3.2. Let $(X,r)$ ...   \n",
       "4996                  iff    By $\\Gamma(x)$ we denote the\\nsubgraph of (th...   \n",
       "5656           if ;if ;if   \\label{Thm:mod 5}\\nFor all $n\\geq0$,\\n\\begin{a...   \n",
       "5657           if ;if ;if   \\label{weighted analog thm }\\nFor all $n\\geq0$...   \n",
       "5688           for;for;for  \\label{thm:alternate thm}\\nFor $n\\geq0$,\\n\\beg...   \n",
       "5689             for ;for   \\label{Kane thm}\\nFor $n\\geq0$,\\n\\begin{align*...   \n",
       "5690                   for  \\label{+--thm}\\nFor all $n\\geq0$,\\n\\begin{alig...   \n",
       "5691               for;for  [Theorem~3 in \\cite{AL}]\\nFor $n>0$,\\n\\begin{a...   \n",
       "5692               for;for  \\nFor $n>0$,\\n\\begin{align}\\nM_{2}(0,4,4n) &>M...   \n",
       "7290                    or  \\n\\label{thm:uniformDegreeBound} \\n\\tGiven a $...   \n",
       "7578       \\text o;\\text o  \\label{diameter}\\nWe have:\\n\\begin{enumerate}[...   \n",
       "8855                    or  \\n\\label{thm:cases}\\nSuppose $S_t$ is a parame...   \n",
       "11231                   if  \\label{THM:mod 25}\\nFor all $n\\geq0$,\\n\\begin{...   \n",
       "11352                   or  \\label{thm:irreducible}\\nLet $\\lambda / \\lambd...   \n",
       "12602              if ;if   \\label{thm:main}\\nLet $A_{1}, A_{2}, \\cdots ,A...   \n",
       "14192   if ; if ; if ; if   \\n\\label{st:th5}\\nLet $\\Gamma$ be a simple con...   \n",
       "14535              if ;if   \\n\\label{4n+1}\\nLet $D = \\{1,j,k\\}$ with $j=4n...   \n",
       "16632                   if  \\label{THM:mod 5}\\nFor all $n\\geq0$,\\n\\begin{a...   \n",
       "16633                   if  \\label{THM:mod 25}\\nFor all $n\\geq0$,\\n\\begin{...   \n",
       "16634                   if  \\label{THM:mod 7}\\nFor all $n\\geq0$,\\n\\begin{a...   \n",
       "16635                   if  \\label{THM:mod 49}\\n\\begin{align}\\n\\Delta_{k}(...   \n",
       "\n",
       "                                               file_name  \\\n",
       "4697                 /home/shufan/que_tex/1805.06575.tex   \n",
       "4698                 /home/shufan/que_tex/1805.06575.tex   \n",
       "4699                 /home/shufan/que_tex/1805.06575.tex   \n",
       "4700                 /home/shufan/que_tex/1805.06575.tex   \n",
       "4741                    /home/shufan/que_tex/Inertia.tex   \n",
       "4990               /home/shufan/que_tex/CYBE30507JSC.tex   \n",
       "4996               /home/shufan/que_tex/CYBE30507JSC.tex   \n",
       "5656                 /home/shufan/que_tex/1706.08223.tex   \n",
       "5657                 /home/shufan/que_tex/1706.08223.tex   \n",
       "5688                 /home/shufan/que_tex/1705.10067.tex   \n",
       "5689                 /home/shufan/que_tex/1705.10067.tex   \n",
       "5690                 /home/shufan/que_tex/1705.10067.tex   \n",
       "5691                 /home/shufan/que_tex/1705.10067.tex   \n",
       "5692                 /home/shufan/que_tex/1705.10067.tex   \n",
       "7290   /home/shufan/que_tex/markovcomplexityDec19-for...   \n",
       "7578           /home/shufan/que_tex/Cone_poset_final.tex   \n",
       "8855        /home/shufan/que_tex/ubiquitous_qps_full.tex   \n",
       "11231                /home/shufan/que_tex/1807.01890.tex   \n",
       "11352            /home/shufan/que_tex/SL2Plethysms8+.tex   \n",
       "12602         /home/shufan/que_tex/t-matchings-final.tex   \n",
       "14192  /home/shufan/que_tex/Stochastic_2016_04_25_AB.tex   \n",
       "14535                /home/shufan/que_tex/1611.03940.tex   \n",
       "16632                /home/shufan/que_tex/1709.02584.tex   \n",
       "16633                /home/shufan/que_tex/1709.02584.tex   \n",
       "16634                /home/shufan/que_tex/1709.02584.tex   \n",
       "16635                /home/shufan/que_tex/1709.02584.tex   \n",
       "\n",
       "            extraction_rule  \\\n",
       "4697      theorem + \\emph{}   \n",
       "4698      theorem + \\emph{}   \n",
       "4699      theorem + \\emph{}   \n",
       "4700      theorem + \\emph{}   \n",
       "4741    theorem + \\textit{}   \n",
       "4990   definition + \\emph{}   \n",
       "4996   definition + \\emph{}   \n",
       "5656      theorem + \\emph{}   \n",
       "5657      theorem + \\emph{}   \n",
       "5688      theorem + \\emph{}   \n",
       "5689      theorem + \\emph{}   \n",
       "5690      theorem + \\emph{}   \n",
       "5691      theorem + \\emph{}   \n",
       "5692      theorem + \\emph{}   \n",
       "7290      theorem + \\emph{}   \n",
       "7578      theorem + \\emph{}   \n",
       "8855      theorem + \\emph{}   \n",
       "11231     theorem + \\emph{}   \n",
       "11352     theorem + \\emph{}   \n",
       "12602     theorem + \\emph{}   \n",
       "14192   theorem + \\textit{}   \n",
       "14535   theorem + \\textit{}   \n",
       "16632     theorem + \\emph{}   \n",
       "16633     theorem + \\emph{}   \n",
       "16634     theorem + \\emph{}   \n",
       "16635     theorem + \\emph{}   \n",
       "\n",
       "                                          plain_text_def      plain_text_term  \\\n",
       "4697   \\nFor all n≥0,\\n\\n    M^*(0,2,n)    >M^*(1,2,n...                if;if   \n",
       "4698   \\nFor all n≥0,\\n\\n    M^*(0,3,n)   >M^*(1,3,n)...                if;if   \n",
       "4699   \\nFor n≥ 1,\\n\\n    M^*(0,3,n)-M^*(1,3,n)=c(n) ...             if;if;if   \n",
       "4700   \\nFor all n≥0,\\n\\n    M^*(0,4,n)   >M^*(2,4,n)...                if;if   \n",
       "4741   \\n\\nLet T be a tree with c(T)≥ 1.\\nThen\\n\\n   ...             if;or;if   \n",
       "4990   \\n <cit.>, 3.2. Let (X,r) be a nondegenerate\\n...                  iff   \n",
       "4996    By Γ(x) we denote the\\nsubgraph of (the\\ncomp...                 iff    \n",
       "5656   \\nFor all n≥0,\\n\\n    w_t(5n+3)≡ w_t(5n+4)≡ 05...          if ;if ;if    \n",
       "5657   \\nFor all n≥0,\\n\\n    c_t(5n+3)= c_t(5n+4)= 0,...          if ;if ;if    \n",
       "5688   \\nFor n≥0,\\n\\n    M_k(0,2,2n)    >M_k(1,2,2n),...          for;for;for   \n",
       "5689   \\nFor n≥0,\\n\\n    M(0,3,3n)    >M(1,3,3n),\\n  ...            for ;for    \n",
       "5690   \\nFor all n≥0,\\n\\n    M_2(0,3,3n)    >M_2(1,3,...                  for   \n",
       "5691   [Theorem 3 in <cit.>]\\nFor n>0,\\n\\n    M(0,4,2...              for;for   \n",
       "5692   \\nFor n>0,\\n\\n    M_2(0,4,4n)    >M_2(2,4,4n)>...              for;for   \n",
       "7290   \\n \\n\\tGiven a k-uniform hypergraph H, the tor...                   or   \n",
       "7578   \\nWe have:\\n\\n\\n  * ((d))=2d for every d∈,\\n\\n...                  o;o   \n",
       "8855   \\n\\nSuppose S_t is a parametric Presburger fam...                   or   \n",
       "11231  \\nFor all n≥0,\\n\\n    Δ_k(125n+99)    ≡025,   ...                   if   \n",
       "11352  \\nLet λ / λ^⋆ be a proper skew partition.\\nThe...                   or   \n",
       "12602  \\nLet A_1, A_2, ⋯ ,A_F be the first F = F_t -1...              if ;if    \n",
       "14192  \\n\\nLet Γ be a simple connected graph of order...   if ; if ; if ; if    \n",
       "14535  \\n\\nLet D = {1,j,k} with j=4n+1, k even, and k...              if ;if    \n",
       "16632  \\nFor all n≥0,\\n\\n    Δ_k(25n+24)    ≡05,   if...                   if   \n",
       "16633  \\nFor all n≥0,\\n\\n    Δ_k(125n+99)    ≡025,   ...                   if   \n",
       "16634  \\nFor all n≥0,\\n\\n    Δ_k(49n+s)≡07,   if   k≡...                   if   \n",
       "16635  \\n\\n    Δ_k(343n+t)≡ 049,   if   k≡171343.\\n\\n...                   if   \n",
       "\n",
       "                                   masked_plain_text_def  \\\n",
       "4697   \\nFor all n≥0,\\n\\n    M^*(0,2,n)    >M^*(1,2,n...   \n",
       "4698   \\nFor all n≥0,\\n\\n    M^*(0,3,n)   >M^*(1,3,n)...   \n",
       "4699   \\nFor n≥ 1,\\n\\n    M^*(0,3,n)-M^*(1,3,n)=c(n) ...   \n",
       "4700   \\nFor all n≥0,\\n\\n    M^*(0,4,n)   >M^*(2,4,n)...   \n",
       "4741   \\n\\nLet T be a tree with c(T)≥ 1.\\nThen\\n\\n   ...   \n",
       "4990   \\n <cit.>, 3.2. Let (X,r) be a nondegenerate\\n...   \n",
       "4996    By Γ(x) we denote the\\nsubgraph of (the\\ncomp...   \n",
       "5656   \\nFor all n≥0,\\n\\n    w_t(5n+3)≡ w_t(5n+4)≡ 05...   \n",
       "5657   \\nFor all n≥0,\\n\\n    c_t(5n+3)= c_t(5n+4)= 0,...   \n",
       "5688   \\nFor n≥0,\\n\\n    M_k(0,2,2n)    >M_k(1,2,2n),...   \n",
       "5689   \\nFor n≥0,\\n\\n    M(0,3,3n)    >M(1,3,3n),\\n  ...   \n",
       "5690   \\nFor all n≥0,\\n\\n    M_2(0,3,3n)    >M_2(1,3,...   \n",
       "5691   [Theorem 3 in <cit.>]\\nFor n>0,\\n\\n    M(0,4,2...   \n",
       "5692   \\nFor n>0,\\n\\n    M_2(0,4,4n)    >M_2(2,4,4n)>...   \n",
       "7290   \\n \\n\\tGiven a k-uniform hypergraph H, the tor...   \n",
       "7578   \\nWe have:\\n\\n\\n  * ((d))=2d for every d∈,\\n\\n...   \n",
       "8855   \\n\\nSuppose S_t is a parametric Presburger fam...   \n",
       "11231  \\nFor all n≥0,\\n\\n    Δ_k(125n+99)    ≡025,   ...   \n",
       "11352  \\nLet λ / λ^⋆ be a proper skew partition.\\nThe...   \n",
       "12602  \\nLet A_1, A_2, ⋯ ,A_F be the first F = F_t -1...   \n",
       "14192  \\n\\nLet Γ be a simple connected graph of order...   \n",
       "14535  \\n\\nLet D = {1,j,k} with j=4n+1, k even, and k...   \n",
       "16632  \\nFor all n≥0,\\n\\n    Δ_k(25n+24)    ≡05,    B...   \n",
       "16633  \\nFor all n≥0,\\n\\n    Δ_k(125n+99)    ≡025,   ...   \n",
       "16634  \\nFor all n≥0,\\n\\n    Δ_k(49n+s)≡07,    B_MATH...   \n",
       "16635  \\n\\n    Δ_k(343n+t)≡ 049,    B_MATH_TERM   k≡1...   \n",
       "\n",
       "                                             labeled_def  \n",
       "4697   O O O O O B_MATH_TERM O O O O O B_MATH_TERM O O O  \n",
       "4698   O O O O O B_MATH_TERM O O O O O B_MATH_TERM O ...  \n",
       "4699   O O O O O O O B_MATH_TERM O O O O B_MATH_TERM ...  \n",
       "4700   O O O O O B_MATH_TERM O O O O O B_MATH_TERM O ...  \n",
       "4741   O O O O O O O O O O O B_MATH_TERM O B_MATH_TER...  \n",
       "4990   O O O O O O O O O O O O O O O O O O O O O B_MA...  \n",
       "4996   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "5656   O O O O O O B_MATH_TERM O O O O B_MATH_TERM O ...  \n",
       "5657   O O O O O O B_MATH_TERM O O O O B_MATH_TERM O ...  \n",
       "5688   O O O O B_MATH_TERM O O O B_MATH_TERM O O O O ...  \n",
       "5689                             O O O O O O O O O O O O  \n",
       "5690   O O O O O O O O O O O O O O O O O O O O O B_MA...  \n",
       "5691   O O O O O O O O B_MATH_TERM O O O B_MATH_TERM ...  \n",
       "5692   O O O O B_MATH_TERM O O O O O O O O O O O B_MA...  \n",
       "7290   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "7578                       O O O O O O O O O O O O O O O  \n",
       "8855   O O O O O O O O O O O O O O O O O O B_MATH_TER...  \n",
       "11231                            O O O O O B_MATH_TERM O  \n",
       "11352  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "12602  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "14192  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "14535  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "16632                            O O O O O B_MATH_TERM O  \n",
       "16633                            O O O O O B_MATH_TERM O  \n",
       "16634                  O O O O B_MATH_TERM O O O O O O O  \n",
       "16635                        O O B_MATH_TERM O O O O O O  "
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#if, for, or\n",
    "df_clean[ df_clean['plain_text_term'].str.match(r'^\\s*([ifor]+\\s*([,;]\\s*[ifor]+\\s*)*)$')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "93696eb8-0a74-45bd-a6b5-0739d735b41c",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean = df_clean[~ df_clean['plain_text_term'].str.match(r'^\\s*([iforIFOR]+\\s*([,;]\\s*[iforIFOR]+\\s*)*)$')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "6093fc04-b698-447a-9100-f06c80c096f8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>term</th>\n",
       "      <th>def</th>\n",
       "      <th>file_name</th>\n",
       "      <th>extraction_rule</th>\n",
       "      <th>plain_text_def</th>\n",
       "      <th>plain_text_term</th>\n",
       "      <th>masked_plain_text_def</th>\n",
       "      <th>labeled_def</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4185</th>\n",
       "      <td>i.e.;I.e.</td>\n",
       "      <td>[Pattern Theorem;~\\cite{Bender1992}]\\n  Suppos...</td>\n",
       "      <td>/home/shufan/que_tex/knotasymp_paper.tex</td>\n",
       "      <td>theorem + \\textit{}</td>\n",
       "      <td>[Pattern Theorem; &lt;cit.&gt;]\\n  Suppose all of th...</td>\n",
       "      <td>i.e.;I.e.</td>\n",
       "      <td>[Pattern Theorem; &lt;cit.&gt;]\\n  Suppose all of th...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O B_MATH_TERM O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14521</th>\n",
       "      <td>I.e.</td>\n",
       "      <td>\\nPOSET is the category (see \\cite{Mac}) whose...</td>\n",
       "      <td>/home/shufan/que_tex/TheRangeofaStOp_revisionf...</td>\n",
       "      <td>definition + \\textit{}</td>\n",
       "      <td>\\nPOSET is the category (see &lt;cit.&gt;) whose obj...</td>\n",
       "      <td>I.e.</td>\n",
       "      <td>\\nPOSET is the category (see &lt;cit.&gt;) whose obj...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O B_MA...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            term                                                def  \\\n",
       "4185   i.e.;I.e.  [Pattern Theorem;~\\cite{Bender1992}]\\n  Suppos...   \n",
       "14521       I.e.  \\nPOSET is the category (see \\cite{Mac}) whose...   \n",
       "\n",
       "                                               file_name  \\\n",
       "4185            /home/shufan/que_tex/knotasymp_paper.tex   \n",
       "14521  /home/shufan/que_tex/TheRangeofaStOp_revisionf...   \n",
       "\n",
       "              extraction_rule  \\\n",
       "4185      theorem + \\textit{}   \n",
       "14521  definition + \\textit{}   \n",
       "\n",
       "                                          plain_text_def plain_text_term  \\\n",
       "4185   [Pattern Theorem; <cit.>]\\n  Suppose all of th...       i.e.;I.e.   \n",
       "14521  \\nPOSET is the category (see <cit.>) whose obj...            I.e.   \n",
       "\n",
       "                                   masked_plain_text_def  \\\n",
       "4185   [Pattern Theorem; <cit.>]\\n  Suppose all of th...   \n",
       "14521  \\nPOSET is the category (see <cit.>) whose obj...   \n",
       "\n",
       "                                             labeled_def  \n",
       "4185   O O O O O O O O O O O O O O O O B_MATH_TERM O ...  \n",
       "14521  O O O O O O O O O O O O O O O O O O O O O B_MA...  "
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_clean[ df_clean['plain_text_term'].str.match(r'^\\s*([IEXiex.]+\\s*([,;]\\s*[IEXiex.]+\\s*)*)$')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "93d97225-232c-4a8a-a015-9f779edad95f",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean = df_clean[~df_clean['plain_text_term'].str.match(r'^\\s*([IEXiex.]+\\s*([,;]\\s*[IEXiex.]+\\s*)*)$')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "cad44ac2-cf7e-4375-aa47-6c008460db0a",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean.to_csv('cleaned_plain-text_term_def_labeled.csv',index=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "bcff7edc-2ab5-40ab-967b-6197c79eda4c",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean = pd.read_csv('cleaned_plain-text_term_def_labeled.csv', delimiter=',')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff03e705-6665-492d-ab42-ebf59adc613a",
   "metadata": {
    "tags": []
   },
   "source": [
    "## update: from \"\\n A graph 𝐺 is \\emph{non}-𝑘-equivalent if...\" the term should be \\emph{non}-𝑘-equivalent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "b11e0b23-3778-4d5a-a22e-01ea6f6607a5",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_19300/2589086422.py:3: UserWarning: This pattern is interpreted as a regular expression, and has match groups. To actually get the groups, use str.extract.\n",
      "  df_clean[df_clean['def'].str.contains(combi_pattern)]\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>term</th>\n",
       "      <th>def</th>\n",
       "      <th>file_name</th>\n",
       "      <th>extraction_rule</th>\n",
       "      <th>plain_text_def</th>\n",
       "      <th>plain_text_term</th>\n",
       "      <th>masked_plain_text_def</th>\n",
       "      <th>labeled_def</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>316</th>\n",
       "      <td>Statement of Theorem \\ref{thm:singleton_b_is_a...</td>\n",
       "      <td>\\n%\\label{thm:singleton_b_is_a_prime}\\n\\emph{S...</td>\n",
       "      <td>/home/shufan/que_tex/1803.03954.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n\\nStatement of Theorem &lt;ref&gt;: Let n be a pos...</td>\n",
       "      <td>Statement of Theorem &lt;ref&gt;</td>\n",
       "      <td>\\n\\nB_MATH_TERM I_MATH_TERM I_MATH_TERM I_MATH...</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM I_MATH_TERM O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>322</th>\n",
       "      <td>weak descent composition of $\\rho$</td>\n",
       "      <td>[\\cite{Ass-T}]\\n  For a reduced word $\\rho$, d...</td>\n",
       "      <td>/home/shufan/que_tex/weak_EG.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>[&lt;cit.&gt;]\\n  For a reduced word ρ, define the w...</td>\n",
       "      <td>weak descent composition of ρ</td>\n",
       "      <td>[&lt;cit.&gt;]\\n  For a reduced word ρ, define the B...</td>\n",
       "      <td>O O O O O O O O B_MATH_TERM I_MATH_TERM I_MATH...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>328</th>\n",
       "      <td>weak descent composition of $T$</td>\n",
       "      <td>[\\cite{Ass-W}]\\n  For a standard key tableau $...</td>\n",
       "      <td>/home/shufan/que_tex/weak_EG.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>[&lt;cit.&gt;]\\n  For a standard key tableau T, defi...</td>\n",
       "      <td>weak descent composition of T</td>\n",
       "      <td>[&lt;cit.&gt;]\\n  For a standard key tableau T, defi...</td>\n",
       "      <td>O O O O O O O O O B_MATH_TERM I_MATH_TERM I_MA...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>702</th>\n",
       "      <td>\\{1,2,3\\;basic matroids</td>\n",
       "      <td>\\label{def:decomposition}\\nA \\emph{\\{1,2,3\\}-...</td>\n",
       "      <td>/home/shufan/que_tex/Decomposition.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nA {1,2,3}-decomposition of a matroid M̃ is ...</td>\n",
       "      <td>{1,2,3 basic matroids</td>\n",
       "      <td>\\nA B_MATH_TERM-decomposition of a matroid M̃...</td>\n",
       "      <td>O O O O O O O O O O O O O O B_MATH_TERM I_MATH...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>731</th>\n",
       "      <td>NP</td>\n",
       "      <td>\\label{t:CTC}\\n{\\sc Common-Tree-Containment} i...</td>\n",
       "      <td>/home/shufan/que_tex/write-up.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nCommon-Tree-Containment is NP-complete when ...</td>\n",
       "      <td>NP</td>\n",
       "      <td>\\nCommon-Tree-Containment is B_MATH_TERM-compl...</td>\n",
       "      <td>O O O O O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14485</th>\n",
       "      <td>ME</td>\n",
       "      <td>\\label{DefMEequivalence}\\nSuppose $\\Sigma$ is ...</td>\n",
       "      <td>/home/shufan/que_tex/1807.06171.tex</td>\n",
       "      <td>definition + \\textit{}</td>\n",
       "      <td>\\nSuppose Σ is an ordered alphabet and w,w'∈Σ^...</td>\n",
       "      <td>ME</td>\n",
       "      <td>\\nSuppose Σ is an ordered alphabet and w,w'∈Σ^...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14523</th>\n",
       "      <td>directed path decomposition;bags;width</td>\n",
       "      <td>\\n\\tLet $D$ be a digraph, $P$ a directed path ...</td>\n",
       "      <td>/home/shufan/que_tex/DMW.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\n\\tLet D be a digraph, P a directed path and ...</td>\n",
       "      <td>directed path decomposition;bags;width</td>\n",
       "      <td>\\n\\tLet D be a digraph, P a directed path and ...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14655</th>\n",
       "      <td>lattice path</td>\n",
       "      <td>\\nA \\emph{lattice path}  of length $n$ is a se...</td>\n",
       "      <td>/home/shufan/que_tex/1112.4026.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nA lattice path  of length n is a sequence (γ...</td>\n",
       "      <td>lattice path</td>\n",
       "      <td>\\nA B_MATH_TERM I_MATH_TERM  of length n is a ...</td>\n",
       "      <td>O B_MATH_TERM I_MATH_TERM O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14740</th>\n",
       "      <td>MSE</td>\n",
       "      <td>\\label{StrongMButNotMSE}\\nSuppose $\\Sigma=\\{a,...</td>\n",
       "      <td>/home/shufan/que_tex/1702.03647.tex</td>\n",
       "      <td>theorem + \\textit{}</td>\n",
       "      <td>\\nSuppose Σ={a,b,c} and w,w'∈Σ^*. Let w=w_0β_1...</td>\n",
       "      <td>MSE</td>\n",
       "      <td>\\nSuppose Σ={a,b,c} and w,w'∈Σ^*. Let w=w_0β_1...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14748</th>\n",
       "      <td>almost strongly elementarily matrix equivalent...</td>\n",
       "      <td>\\label{DefineMSAE}\\nSuppose $\\Sigma=\\{a,b,c\\}$...</td>\n",
       "      <td>/home/shufan/que_tex/1702.03647.tex</td>\n",
       "      <td>definition + \\textit{}</td>\n",
       "      <td>\\nSuppose Σ={a,b,c} and w,w'∈Σ^*. We say that ...</td>\n",
       "      <td>almost strongly elementarily matrix equivalent...</td>\n",
       "      <td>\\nSuppose Σ={a,b,c} and w,w'∈Σ^*. We say that ...</td>\n",
       "      <td>O O O O O O O O O O O B_MATH_TERM I_MATH_TERM ...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>82 rows × 8 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                    term  \\\n",
       "316    Statement of Theorem \\ref{thm:singleton_b_is_a...   \n",
       "322                   weak descent composition of $\\rho$   \n",
       "328                      weak descent composition of $T$   \n",
       "702                              \\{1,2,3\\;basic matroids   \n",
       "731                                                   NP   \n",
       "...                                                  ...   \n",
       "14485                                                 ME   \n",
       "14523             directed path decomposition;bags;width   \n",
       "14655                                       lattice path   \n",
       "14740                                                MSE   \n",
       "14748  almost strongly elementarily matrix equivalent...   \n",
       "\n",
       "                                                     def  \\\n",
       "316    \\n%\\label{thm:singleton_b_is_a_prime}\\n\\emph{S...   \n",
       "322    [\\cite{Ass-T}]\\n  For a reduced word $\\rho$, d...   \n",
       "328    [\\cite{Ass-W}]\\n  For a standard key tableau $...   \n",
       "702     \\label{def:decomposition}\\nA \\emph{\\{1,2,3\\}-...   \n",
       "731    \\label{t:CTC}\\n{\\sc Common-Tree-Containment} i...   \n",
       "...                                                  ...   \n",
       "14485  \\label{DefMEequivalence}\\nSuppose $\\Sigma$ is ...   \n",
       "14523  \\n\\tLet $D$ be a digraph, $P$ a directed path ...   \n",
       "14655  \\nA \\emph{lattice path}  of length $n$ is a se...   \n",
       "14740  \\label{StrongMButNotMSE}\\nSuppose $\\Sigma=\\{a,...   \n",
       "14748  \\label{DefineMSAE}\\nSuppose $\\Sigma=\\{a,b,c\\}$...   \n",
       "\n",
       "                                    file_name         extraction_rule  \\\n",
       "316       /home/shufan/que_tex/1803.03954.tex       theorem + \\emph{}   \n",
       "322          /home/shufan/que_tex/weak_EG.tex    definition + \\emph{}   \n",
       "328          /home/shufan/que_tex/weak_EG.tex    definition + \\emph{}   \n",
       "702    /home/shufan/que_tex/Decomposition.tex    definition + \\emph{}   \n",
       "731         /home/shufan/que_tex/write-up.tex       theorem + \\emph{}   \n",
       "...                                       ...                     ...   \n",
       "14485     /home/shufan/que_tex/1807.06171.tex  definition + \\textit{}   \n",
       "14523            /home/shufan/que_tex/DMW.tex    definition + \\emph{}   \n",
       "14655      /home/shufan/que_tex/1112.4026.tex    definition + \\emph{}   \n",
       "14740     /home/shufan/que_tex/1702.03647.tex     theorem + \\textit{}   \n",
       "14748     /home/shufan/que_tex/1702.03647.tex  definition + \\textit{}   \n",
       "\n",
       "                                          plain_text_def  \\\n",
       "316    \\n\\nStatement of Theorem <ref>: Let n be a pos...   \n",
       "322    [<cit.>]\\n  For a reduced word ρ, define the w...   \n",
       "328    [<cit.>]\\n  For a standard key tableau T, defi...   \n",
       "702     \\nA {1,2,3}-decomposition of a matroid M̃ is ...   \n",
       "731    \\nCommon-Tree-Containment is NP-complete when ...   \n",
       "...                                                  ...   \n",
       "14485  \\nSuppose Σ is an ordered alphabet and w,w'∈Σ^...   \n",
       "14523  \\n\\tLet D be a digraph, P a directed path and ...   \n",
       "14655  \\nA lattice path  of length n is a sequence (γ...   \n",
       "14740  \\nSuppose Σ={a,b,c} and w,w'∈Σ^*. Let w=w_0β_1...   \n",
       "14748  \\nSuppose Σ={a,b,c} and w,w'∈Σ^*. We say that ...   \n",
       "\n",
       "                                         plain_text_term  \\\n",
       "316                           Statement of Theorem <ref>   \n",
       "322                        weak descent composition of ρ   \n",
       "328                        weak descent composition of T   \n",
       "702                                {1,2,3 basic matroids   \n",
       "731                                                   NP   \n",
       "...                                                  ...   \n",
       "14485                                                 ME   \n",
       "14523             directed path decomposition;bags;width   \n",
       "14655                                       lattice path   \n",
       "14740                                                MSE   \n",
       "14748  almost strongly elementarily matrix equivalent...   \n",
       "\n",
       "                                   masked_plain_text_def  \\\n",
       "316    \\n\\nB_MATH_TERM I_MATH_TERM I_MATH_TERM I_MATH...   \n",
       "322    [<cit.>]\\n  For a reduced word ρ, define the B...   \n",
       "328    [<cit.>]\\n  For a standard key tableau T, defi...   \n",
       "702     \\nA B_MATH_TERM-decomposition of a matroid M̃...   \n",
       "731    \\nCommon-Tree-Containment is B_MATH_TERM-compl...   \n",
       "...                                                  ...   \n",
       "14485  \\nSuppose Σ is an ordered alphabet and w,w'∈Σ^...   \n",
       "14523  \\n\\tLet D be a digraph, P a directed path and ...   \n",
       "14655  \\nA B_MATH_TERM I_MATH_TERM  of length n is a ...   \n",
       "14740  \\nSuppose Σ={a,b,c} and w,w'∈Σ^*. Let w=w_0β_1...   \n",
       "14748  \\nSuppose Σ={a,b,c} and w,w'∈Σ^*. We say that ...   \n",
       "\n",
       "                                             labeled_def  \n",
       "316    B_MATH_TERM I_MATH_TERM I_MATH_TERM O O O O O ...  \n",
       "322    O O O O O O O O B_MATH_TERM I_MATH_TERM I_MATH...  \n",
       "328    O O O O O O O O O B_MATH_TERM I_MATH_TERM I_MA...  \n",
       "702    O O O O O O O O O O O O O O B_MATH_TERM I_MATH...  \n",
       "731                              O O O O O O O O O O O O  \n",
       "...                                                  ...  \n",
       "14485  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "14523  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "14655  O B_MATH_TERM I_MATH_TERM O O O O O O O O O O ...  \n",
       "14740  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "14748  O O O O O O O O O O O B_MATH_TERM I_MATH_TERM ...  \n",
       "\n",
       "[82 rows x 8 columns]"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "combi_pattern = r'(\\\\emph\\{.*?\\}-)|(\\\\textit\\{.*?\\}-)'\n",
    "\n",
    "df_clean[df_clean['def'].str.contains(combi_pattern)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "33545aec-9bf1-4d93-b0e9-2128e22123d1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This is some text with B_MATH_TERM I_MATH_TERM I_MATH_TERM I_MATH_TERM I_MATH_TERM I_MATH_TERM in it. B_MATH_TERM . B_MATH_TERM I_MATH_TERM please. \\n A graph 𝐺 is B_MATH_TERM if...\n"
     ]
    }
   ],
   "source": [
    "def mask_emph_and_tail(text):\n",
    "    pattern = r'\\\\emph\\{(.*?)\\}(-\\S*)?'\n",
    "\n",
    "    def replace(match):\n",
    "        words = match.group(1).split()\n",
    "        if not words:\n",
    "            return ''\n",
    "        masked_words = ['B_MATH_TERM'] + ['I_MATH_TERM'] * (len(words) - 1)\n",
    "        return ' '.join(masked_words)\n",
    "    return re.sub(pattern, replace, text)\n",
    "\n",
    "# Example usage\n",
    "text = r'This is some text with \\emph{emphasized words A B C D} in it. \\emph{blah} . \\emph{blah blah}-mask_me, please. \\n A graph 𝐺 is \\emph{non}-𝑘-equivalent if...'\n",
    "masked_text = mask_emph_and_tail(text)\n",
    "print(masked_text)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "1e2178b0-22f2-4048-b34c-419a00a2adfc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This is some text with B_MATH_TERM I_MATH_TERM I_MATH_TERM I_MATH_TERM I_MATH_TERM I_MATH_TERM in it. B_MATH_TERM. B_MATH_TERM I_MATH_TERM please. \\n A graph 𝐺 is B_MATH_TERM if...\n"
     ]
    }
   ],
   "source": [
    "def mask_textit_and_tail(text):\n",
    "    pattern = r'\\\\textit\\{(.*?)\\}(-\\S*)?'\n",
    "\n",
    "    def replace(match):\n",
    "        words = match.group(1).split()\n",
    "        if not words:\n",
    "            return ''\n",
    "        masked_words = ['B_MATH_TERM'] + ['I_MATH_TERM'] * (len(words) - 1)\n",
    "        return ' '.join(masked_words)\n",
    "    return re.sub(pattern, replace, text)\n",
    "\n",
    "# Example usage\n",
    "text = r'This is some text with \\textit{emphasized words A B C D} in it. \\textit{blah}. \\textit{blah blah}-mask_me, please. \\n A graph 𝐺 is \\textit{non}-𝑘-equivalent if...'\n",
    "masked_text = mask_textit_and_tail(text)\n",
    "print(masked_text)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "45bfbdbf-459b-4ad7-b43f-e6ee7e3d0dc2",
   "metadata": {},
   "outputs": [],
   "source": [
    "def mask_def_sentence_update_tail(sent, extraction_rule, masked_plain_text_def, term=''):\n",
    "    combi_pattern = r'(\\\\emph\\{.*?\\}-)|(\\\\textit\\{.*?\\}-)'\n",
    "\n",
    "    if re.search(combi_pattern, sent):\n",
    "        if 'emph' in extraction_rule:\n",
    "            masked_text = mask_emph_and_tail(sent)\n",
    "            return LatexNodes2Text().latex_to_text(masked_text) # convert to plain text\n",
    "        elif 'textit' in extraction_rule:\n",
    "            masked_text = mask_textit_and_tail(sent)\n",
    "            return LatexNodes2Text().latex_to_text(masked_text) # convert to plain text\n",
    "        else:\n",
    "            return masked_plain_text_def\n",
    "    else:\n",
    "        return masked_plain_text_def\n",
    "    \n",
    "\n",
    "df_clean['masked_plain_text_def'] = df_clean.apply(lambda x: mask_def_sentence_update_tail(x['def'], x['extraction_rule'], x['masked_plain_text_def'], x['term']), axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "c47372a4-3326-4444-b3bf-8666e48d8445",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean['labeled_def'] = df_clean['masked_plain_text_def'].apply(label_text)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "9e28d573-7d85-4d54-b6bf-d896c3dab8b2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "blah blah;emphasized words A B C D;blah;blah blah-bibi\n"
     ]
    }
   ],
   "source": [
    "def extract_textit_combi_terms(text):\n",
    "    pattern = r'\\\\textit\\{(.*?)\\}(-\\S*)?'\n",
    "    matches = re.findall(pattern, text)\n",
    "    result = []\n",
    "    for match in matches:\n",
    "        result.append(''.join(match))\n",
    "    return ';'.join(result)\n",
    "# Example usage\n",
    "text = r'\\textit{blah blah}! This is some text with \\textit{emphasized words A B C D}, in it. \\textit{blah}. \\textit{blah blah}-bibi is a combi. '\n",
    "masked_text = extract_textit_combi_terms(text)\n",
    "print(masked_text)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "d8072cef-62cf-454c-9c9f-b2e5563d0d9c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "blah blah;emphasized words A B C D;blah;blah blah-bibi\n"
     ]
    }
   ],
   "source": [
    "def extract_emph_combi_terms(text):\n",
    "    pattern = r'\\\\emph\\{(.*?)\\}(-\\S*)?'\n",
    "    matches = re.findall(pattern, text)\n",
    "    result = []\n",
    "    for match in matches:\n",
    "        result.append(''.join(match))\n",
    "    return ';'.join(result)\n",
    "# Example usage\n",
    "text = r'\\emph{blah blah}! This is some text with \\emph{emphasized words A B C D}, in it. \\emph{blah}. \\emph{blah blah}-bibi is a combi. '\n",
    "masked_text = extract_emph_combi_terms(text)\n",
    "print(masked_text)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "7ddf5e5f-0cc3-4f2b-8dae-7598bfebb534",
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_combi_terms(sent, extraction_rule, term):\n",
    "    combi_pattern = r'(\\\\emph\\{.*?\\}-)|(\\\\textit\\{.*?\\}-)'\n",
    "    if re.search(combi_pattern, sent):\n",
    "        if 'emph' in extraction_rule:\n",
    "            combi_term = extract_emph_combi_terms(sent)\n",
    "            return combi_term\n",
    "        elif 'textit' in extraction_rule:\n",
    "            combi_term = extract_textit_combi_terms(sent)\n",
    "            return combi_term\n",
    "        else:\n",
    "            return term\n",
    "    else:\n",
    "        return term\n",
    "    \n",
    "\n",
    "df_clean['term'] = df_clean.apply(lambda x: update_combi_terms(x['def'], x['extraction_rule'], x['term']), axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "5bcbd7ee-1636-4628-8fbd-87240caad3cc",
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_plain_text_combi_terms(sent, term, plain_text_term):\n",
    "    combi_pattern = r'(\\\\emph\\{.*?\\}-)|(\\\\textit\\{.*?\\}-)'\n",
    "    if re.search(combi_pattern, sent):\n",
    "        return LatexNodes2Text().latex_to_text(term)\n",
    "    else:\n",
    "        return plain_text_term\n",
    "    \n",
    "\n",
    "df_clean['plain_text_term'] = df_clean.apply(lambda x: update_plain_text_combi_terms(x['def'], x['term'], x['plain_text_term']), axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "afa50810-5aac-48a6-b241-1c6cd8bf0a49",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_19300/2504376093.py:1: UserWarning: This pattern is interpreted as a regular expression, and has match groups. To actually get the groups, use str.extract.\n",
      "  df_clean[df_clean['def'].str.contains(combi_pattern)].to_csv(\"combis_0717.csv\")\n"
     ]
    }
   ],
   "source": [
    "df_clean[df_clean['def'].str.contains(combi_pattern)].to_csv(\"combis_0717.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "2ae13392-3205-4133-9195-288805a62000",
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>term</th>\n",
       "      <th>def</th>\n",
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       "    <tr>\n",
       "      <th>7448</th>\n",
       "      <td>no</td>\n",
       "      <td>[Schwenk]\\label{t:S} Let $1\\leq m\\leq n$. The ...</td>\n",
       "      <td>/home/shufan/que_tex/Knight.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>[Schwenk] Let 1≤ m≤ n. The m× n\\n  chessboard ...</td>\n",
       "      <td>no</td>\n",
       "      <td>[Schwenk] Let 1≤ m≤ n. The m× n\\n  chessboard ...</td>\n",
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       "      <td>no</td>\n",
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       "      <td>/home/shufan/que_tex/Knight.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>[DeMaio and Mathew] Let 2≤ m≤ n≤\\n  p.  The m×...</td>\n",
       "      <td>no</td>\n",
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       "      <th>7450</th>\n",
       "      <td>no</td>\n",
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       "      <td>/home/shufan/que_tex/Knight.tex</td>\n",
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       "      <td>\\nLet 2≤ n_1≤ n_2≤... ≤ n_k, with k≥ 3. The\\nn...</td>\n",
       "      <td>no</td>\n",
       "      <td>\\nLet 2≤ n_1≤ n_2≤... ≤ n_k, with k≥ 3. The\\nn...</td>\n",
       "      <td>O O O O O O O O O O O O O O B_MATH_TERM O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7645</th>\n",
       "      <td>n;n;n;n</td>\n",
       "      <td>(\\cite[Proposition 4, 5, 6, 7, 8, 9 $\\&amp;$ 10]{...</td>\n",
       "      <td>/home/shufan/que_tex/1402.0615.tex</td>\n",
       "      <td>theorem + \\textit{}</td>\n",
       "      <td>(&lt;cit.&gt;) \\n\\n\\n  * Let P_n be a path of the s...</td>\n",
       "      <td>n;n;n;n</td>\n",
       "      <td>(&lt;cit.&gt;) \\n\\n\\n  * Let P_n be a path of the s...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         term                                                def  \\\n",
       "7448       no  [Schwenk]\\label{t:S} Let $1\\leq m\\leq n$. The ...   \n",
       "7449       no  [DeMaio and Mathew]\\label{t:DeM} Let $2\\leq m\\...   \n",
       "7450       no  \\label{t:main}\\nLet $2\\leq n_1\\leq n_2\\leq... ...   \n",
       "7645  n;n;n;n   (\\cite[Proposition 4, 5, 6, 7, 8, 9 $\\&$ 10]{...   \n",
       "\n",
       "                               file_name      extraction_rule  \\\n",
       "7448     /home/shufan/que_tex/Knight.tex    theorem + \\emph{}   \n",
       "7449     /home/shufan/que_tex/Knight.tex    theorem + \\emph{}   \n",
       "7450     /home/shufan/que_tex/Knight.tex    theorem + \\emph{}   \n",
       "7645  /home/shufan/que_tex/1402.0615.tex  theorem + \\textit{}   \n",
       "\n",
       "                                         plain_text_def plain_text_term  \\\n",
       "7448  [Schwenk] Let 1≤ m≤ n. The m× n\\n  chessboard ...              no   \n",
       "7449  [DeMaio and Mathew] Let 2≤ m≤ n≤\\n  p.  The m×...              no   \n",
       "7450  \\nLet 2≤ n_1≤ n_2≤... ≤ n_k, with k≥ 3. The\\nn...              no   \n",
       "7645   (<cit.>) \\n\\n\\n  * Let P_n be a path of the s...         n;n;n;n   \n",
       "\n",
       "                                  masked_plain_text_def  \\\n",
       "7448  [Schwenk] Let 1≤ m≤ n. The m× n\\n  chessboard ...   \n",
       "7449  [DeMaio and Mathew] Let 2≤ m≤ n≤\\n  p.  The m×...   \n",
       "7450  \\nLet 2≤ n_1≤ n_2≤... ≤ n_k, with k≥ 3. The\\nn...   \n",
       "7645   (<cit.>) \\n\\n\\n  * Let P_n be a path of the s...   \n",
       "\n",
       "                                            labeled_def  \n",
       "7448  O O O O O O O O O O B_MATH_TERM O O O O O O O ...  \n",
       "7449  O O O O O O O O O O O O O O B_MATH_TERM O O O ...  \n",
       "7450  O O O O O O O O O O O O O O B_MATH_TERM O O O ...  \n",
       "7645  O O O O O O O O O O O O O O O O O O O O O O O ...  "
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# no\n",
    "df_clean[ df_clean['plain_text_term'].str.match(r'^\\s*([noNO]+\\s*([,;]\\s*[noNO]+\\s*)*)$')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "666efa50-5520-4443-aef3-760ae25364bc",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean = df_clean[ ~df_clean['plain_text_term'].str.match(r'^\\s*([noNO]+\\s*([,;]\\s*[noNO]+\\s*)*)$')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "c113a74f-8a6a-40fc-8207-264e6f42db04",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>term</th>\n",
       "      <th>def</th>\n",
       "      <th>file_name</th>\n",
       "      <th>extraction_rule</th>\n",
       "      <th>plain_text_def</th>\n",
       "      <th>plain_text_term</th>\n",
       "      <th>masked_plain_text_def</th>\n",
       "      <th>labeled_def</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>192</th>\n",
       "      <td>(P2), (P3), (P4)</td>\n",
       "      <td>\\label{Correctness of ASE}\\nThe association sc...</td>\n",
       "      <td>/home/shufan/que_tex/Extensibility.tex</td>\n",
       "      <td>theorem + \\textit{}</td>\n",
       "      <td>\\nThe association scheme extension algorithm w...</td>\n",
       "      <td>(P2), (P3), (P4)</td>\n",
       "      <td>\\nThe association scheme extension algorithm w...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>293</th>\n",
       "      <td>$\\Comp{(n)}$</td>\n",
       "      <td>Let $\\Comp(n)$ denote the poset of ordered int...</td>\n",
       "      <td>/home/shufan/que_tex/alpha_colored_may_27.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>Let (n) denote the poset of ordered integer pa...</td>\n",
       "      <td>(n)</td>\n",
       "      <td>Let (n) denote the poset of ordered integer pa...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>803</th>\n",
       "      <td>(TB);(i);(ii)</td>\n",
       "      <td>[Kriesell~\\cite{Kriesell:1325227}] \\label{T5}\\...</td>\n",
       "      <td>/home/shufan/que_tex/double-col-critical_prepr...</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>[Kriesell &lt;cit.&gt;] \\n  A graph is a minimal cri...</td>\n",
       "      <td>(TB);(i);(ii)</td>\n",
       "      <td>[Kriesell &lt;cit.&gt;] \\n  A graph is a minimal cri...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3140</th>\n",
       "      <td>(a);(b);(c)</td>\n",
       "      <td>\\label{th:logconc-a}\\nSuppose $x\\in(0,1)$ is f...</td>\n",
       "      <td>/home/shufan/que_tex/1509.05120.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nSuppose x∈(0,1) is fixed. Then:\\n\\n(a) if 0&lt;...</td>\n",
       "      <td>(a);(b);(c)</td>\n",
       "      <td>\\nSuppose x∈(0,1) is fixed. Then:\\n\\nB_MATH_TE...</td>\n",
       "      <td>O O O O O B_MATH_TERM O O O O O O O O O O B_MA...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4245</th>\n",
       "      <td>(a);(b)</td>\n",
       "      <td>\\label{thm:foulkes}\\n \\emph{(a)} Let $\\mu\\vda...</td>\n",
       "      <td>/home/shufan/que_tex/submission.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n (a) Let μ⊢ n, where n=2k+1. Then\\n  \\n    ...</td>\n",
       "      <td>(a);(b)</td>\n",
       "      <td>\\n B_MATH_TERM Let μ⊢ n, where n=2k+1. Then\\n...</td>\n",
       "      <td>B_MATH_TERM O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4246</th>\n",
       "      <td>(a);(b);(c);(d)</td>\n",
       "      <td>\\label{thm:bn}\\n\\emph{(a)} If $n$ is odd then...</td>\n",
       "      <td>/home/shufan/que_tex/submission.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n(a) If n is odd then\\n  \\n    b(n) = b^∗(n)...</td>\n",
       "      <td>(a);(b);(c);(d)</td>\n",
       "      <td>\\nB_MATH_TERM If n is odd then\\n  \\n    b(n) ...</td>\n",
       "      <td>B_MATH_TERM O O O O O O O O O O O B_MATH_TERM ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7355</th>\n",
       "      <td>(a);(i);(ii);(b)</td>\n",
       "      <td>\\label{IB_Freezing}\\n{Let $k\\geq 3$. There exi...</td>\n",
       "      <td>/home/shufan/que_tex/1808.04060.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet k≥ 3. There exists  0&lt;ϵ_q=o_q(1) and pos...</td>\n",
       "      <td>(a);(i);(ii);(b)</td>\n",
       "      <td>\\nLet k≥ 3. There exists  0&lt;ϵ_q=o_q(1) and pos...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8059</th>\n",
       "      <td>(b);(c)</td>\n",
       "      <td>\\n\\label{grids}\\n\\n\\begin{enumerate}\\n\\item[(a...</td>\n",
       "      <td>/home/shufan/que_tex/ProtectionSurvey_Klosterm...</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n\\n\\n\\n\\n  (a) τ_m^∞(P_1 P_n)=n-1.\\n\\n\\n\\n   ...</td>\n",
       "      <td>(b);(c)</td>\n",
       "      <td>\\n\\n\\n\\n\\n  (a) τ_m^∞(P_1 P_n)=n-1.\\n\\n\\n\\n   ...</td>\n",
       "      <td>O O O B_MATH_TERM O O O O O O O O O B_MATH_TER...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9041</th>\n",
       "      <td>(Furstenberg)</td>\n",
       "      <td>\\emph{(Furstenberg)}\\n\\label{furst1}\\nLet $\\ka...</td>\n",
       "      <td>/home/shufan/que_tex/1505.01379.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>(Furstenberg)\\n\\nLet κ be a field of positive ...</td>\n",
       "      <td>(Furstenberg)</td>\n",
       "      <td>B_MATH_TERM\\n\\nLet κ be a field of positive ch...</td>\n",
       "      <td>B_MATH_TERM O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9042</th>\n",
       "      <td>(Furstenberg)</td>\n",
       "      <td>\\emph{(Furstenberg)}\\n\\label{furst2}\\nLet $\\ma...</td>\n",
       "      <td>/home/shufan/que_tex/1505.01379.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>(Furstenberg)\\n\\nLet 𝔽_q be a finite field of ...</td>\n",
       "      <td>(Furstenberg)</td>\n",
       "      <td>B_MATH_TERM\\n\\nLet 𝔽_q be a finite field of ch...</td>\n",
       "      <td>B_MATH_TERM O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9043</th>\n",
       "      <td>(Christol)</td>\n",
       "      <td>\\emph{(Christol)}\\n\\label{christol}\\nLet $\\mat...</td>\n",
       "      <td>/home/shufan/que_tex/1505.01379.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>(Christol)\\n\\nLet 𝔽_q be a finite field of cha...</td>\n",
       "      <td>(Christol)</td>\n",
       "      <td>B_MATH_TERM\\n\\nLet 𝔽_q be a finite field of ch...</td>\n",
       "      <td>B_MATH_TERM O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9534</th>\n",
       "      <td>(a);(b)</td>\n",
       "      <td>\\label{thm:equalDegree}\\nLet $\\nlambda$ and $\\...</td>\n",
       "      <td>/home/shufan/que_tex/SL2Plethysms8+.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet  and  be partitions and let ℓ≥ℓ(λ), ℓ(μ)...</td>\n",
       "      <td>(a);(b)</td>\n",
       "      <td>\\nLet  and  be partitions and let ℓ≥ℓ(λ), ℓ(μ)...</td>\n",
       "      <td>O O O O O O O O B_MATH_TERM O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9535</th>\n",
       "      <td>(d);(e);(g)</td>\n",
       "      <td>\\label{thm:eqvConds}\\nLet $\\lambda$ and $\\mu$ ...</td>\n",
       "      <td>/home/shufan/que_tex/SL2Plethysms8+.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet λ and μ be partitions and let ℓ, m ∈ be ...</td>\n",
       "      <td>(d);(e);(g)</td>\n",
       "      <td>\\nLet λ and μ be partitions and let ℓ, m ∈ be ...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9976</th>\n",
       "      <td>(H1);(H2);(H4);(H7);(H8);(H3);(H5);(H6)</td>\n",
       "      <td>\\n\\thmlabel{hickman}\\nThe system\\n$\\mathcal{H}...</td>\n",
       "      <td>/home/shufan/que_tex/1007.3120.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nhickman\\nThe system\\nℋ = {(H1) , (H2) , (H4)...</td>\n",
       "      <td>(H1);(H2);(H4);(H7);(H8);(H3);(H5);(H6)</td>\n",
       "      <td>\\nhickman\\nThe system\\nℋ = {B_MATH_TERM , B_MA...</td>\n",
       "      <td>O O O O O O O B_MATH_TERM O B_MATH_TERM O B_MA...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11305</th>\n",
       "      <td>(b)</td>\n",
       "      <td>\\label{straight}\\n\\begin{itemize}\\n\\item[(a)] ...</td>\n",
       "      <td>/home/shufan/que_tex/1304.7039.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n\\n\\n  (a) The standard bitableaux are a K-ve...</td>\n",
       "      <td>(b)</td>\n",
       "      <td>\\n\\n\\n  (a) The standard bitableaux are a K-ve...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12213</th>\n",
       "      <td>(Rado)</td>\n",
       "      <td>\\textit{(Rado)}\\nA system of linear equations ...</td>\n",
       "      <td>/home/shufan/que_tex/0711.3050.tex</td>\n",
       "      <td>theorem + \\textit{}</td>\n",
       "      <td>(Rado)\\nA system of linear equations is regula...</td>\n",
       "      <td>(Rado)</td>\n",
       "      <td>B_MATH_TERM\\nA system of linear equations is r...</td>\n",
       "      <td>B_MATH_TERM O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14243</th>\n",
       "      <td>(a);(b);(c)</td>\n",
       "      <td>\\label{theo:BST_occupation_numbers}\\nLet $(\\LL...</td>\n",
       "      <td>/home/shufan/que_tex/edgeworth_random_trees-4.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet (_n(k))_k∈ be the  external profile of a...</td>\n",
       "      <td>(a);(b);(c)</td>\n",
       "      <td>\\nLet (_n(k))_k∈ be the  external profile of a...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14244</th>\n",
       "      <td>(a);(b);(c)</td>\n",
       "      <td>\\label{theo:L_n_lim_distr_all_together}\\nConsi...</td>\n",
       "      <td>/home/shufan/que_tex/edgeworth_random_trees-4.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nConsider a one-split BRW with deterministic ...</td>\n",
       "      <td>(a);(b);(c)</td>\n",
       "      <td>\\nConsider a one-split BRW with deterministic ...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O B_MATH_T...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14245</th>\n",
       "      <td>(a);(b);(b);(c)</td>\n",
       "      <td>\\label{theo:BST_occupation_numbers_logn_case}\\...</td>\n",
       "      <td>/home/shufan/que_tex/edgeworth_random_trees-4.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet (_n(k))_k∈ be the profile of a random bi...</td>\n",
       "      <td>(a);(b);(b);(c)</td>\n",
       "      <td>\\nLet (_n(k))_k∈ be the profile of a random bi...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O B_MA...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14531</th>\n",
       "      <td>(Stanley)</td>\n",
       "      <td>\\n\\emph{(Stanley)} \\cite{stanleycd} Let $\\Omeg...</td>\n",
       "      <td>/home/shufan/que_tex/SubdivisionCDdecompositio...</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n(Stanley) &lt;cit.&gt; Let Ω be an S-shellable reg...</td>\n",
       "      <td>(Stanley)</td>\n",
       "      <td>\\nB_MATH_TERM &lt;cit.&gt; Let Ω be an S-shellable r...</td>\n",
       "      <td>B_MATH_TERM O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14536</th>\n",
       "      <td>(Stanley)</td>\n",
       "      <td>\\emph{(Stanley)}Let $P$ be the face poset of ...</td>\n",
       "      <td>/home/shufan/que_tex/SubdivisionCDdecompositio...</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>(Stanley)Let P be the face poset of a rationa...</td>\n",
       "      <td>(Stanley)</td>\n",
       "      <td>B_MATH_TERMLet P be the face poset of a ratio...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14537</th>\n",
       "      <td>(Stanley)</td>\n",
       "      <td>\\emph{(Stanley)} Let $P$ be a rational $d$-po...</td>\n",
       "      <td>/home/shufan/que_tex/SubdivisionCDdecompositio...</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>(Stanley) Let P be a rational d-polytope. Sup...</td>\n",
       "      <td>(Stanley)</td>\n",
       "      <td>B_MATH_TERM Let P be a rational d-polytope. S...</td>\n",
       "      <td>B_MATH_TERM O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                          term  \\\n",
       "192                           (P2), (P3), (P4)   \n",
       "293                               $\\Comp{(n)}$   \n",
       "803                              (TB);(i);(ii)   \n",
       "3140                               (a);(b);(c)   \n",
       "4245                                   (a);(b)   \n",
       "4246                           (a);(b);(c);(d)   \n",
       "7355                          (a);(i);(ii);(b)   \n",
       "8059                                   (b);(c)   \n",
       "9041                             (Furstenberg)   \n",
       "9042                             (Furstenberg)   \n",
       "9043                                (Christol)   \n",
       "9534                                   (a);(b)   \n",
       "9535                               (d);(e);(g)   \n",
       "9976   (H1);(H2);(H4);(H7);(H8);(H3);(H5);(H6)   \n",
       "11305                                      (b)   \n",
       "12213                                   (Rado)   \n",
       "14243                              (a);(b);(c)   \n",
       "14244                              (a);(b);(c)   \n",
       "14245                          (a);(b);(b);(c)   \n",
       "14531                                (Stanley)   \n",
       "14536                                (Stanley)   \n",
       "14537                                (Stanley)   \n",
       "\n",
       "                                                     def  \\\n",
       "192    \\label{Correctness of ASE}\\nThe association sc...   \n",
       "293    Let $\\Comp(n)$ denote the poset of ordered int...   \n",
       "803    [Kriesell~\\cite{Kriesell:1325227}] \\label{T5}\\...   \n",
       "3140   \\label{th:logconc-a}\\nSuppose $x\\in(0,1)$ is f...   \n",
       "4245    \\label{thm:foulkes}\\n \\emph{(a)} Let $\\mu\\vda...   \n",
       "4246    \\label{thm:bn}\\n\\emph{(a)} If $n$ is odd then...   \n",
       "7355   \\label{IB_Freezing}\\n{Let $k\\geq 3$. There exi...   \n",
       "8059   \\n\\label{grids}\\n\\n\\begin{enumerate}\\n\\item[(a...   \n",
       "9041   \\emph{(Furstenberg)}\\n\\label{furst1}\\nLet $\\ka...   \n",
       "9042   \\emph{(Furstenberg)}\\n\\label{furst2}\\nLet $\\ma...   \n",
       "9043   \\emph{(Christol)}\\n\\label{christol}\\nLet $\\mat...   \n",
       "9534   \\label{thm:equalDegree}\\nLet $\\nlambda$ and $\\...   \n",
       "9535   \\label{thm:eqvConds}\\nLet $\\lambda$ and $\\mu$ ...   \n",
       "9976   \\n\\thmlabel{hickman}\\nThe system\\n$\\mathcal{H}...   \n",
       "11305  \\label{straight}\\n\\begin{itemize}\\n\\item[(a)] ...   \n",
       "12213  \\textit{(Rado)}\\nA system of linear equations ...   \n",
       "14243  \\label{theo:BST_occupation_numbers}\\nLet $(\\LL...   \n",
       "14244  \\label{theo:L_n_lim_distr_all_together}\\nConsi...   \n",
       "14245  \\label{theo:BST_occupation_numbers_logn_case}\\...   \n",
       "14531  \\n\\emph{(Stanley)} \\cite{stanleycd} Let $\\Omeg...   \n",
       "14536   \\emph{(Stanley)}Let $P$ be the face poset of ...   \n",
       "14537   \\emph{(Stanley)} Let $P$ be a rational $d$-po...   \n",
       "\n",
       "                                               file_name      extraction_rule  \\\n",
       "192               /home/shufan/que_tex/Extensibility.tex  theorem + \\textit{}   \n",
       "293        /home/shufan/que_tex/alpha_colored_may_27.tex         definition[]   \n",
       "803    /home/shufan/que_tex/double-col-critical_prepr...    theorem + \\emph{}   \n",
       "3140                 /home/shufan/que_tex/1509.05120.tex    theorem + \\emph{}   \n",
       "4245                 /home/shufan/que_tex/submission.tex    theorem + \\emph{}   \n",
       "4246                 /home/shufan/que_tex/submission.tex    theorem + \\emph{}   \n",
       "7355                 /home/shufan/que_tex/1808.04060.tex    theorem + \\emph{}   \n",
       "8059   /home/shufan/que_tex/ProtectionSurvey_Klosterm...    theorem + \\emph{}   \n",
       "9041                 /home/shufan/que_tex/1505.01379.tex    theorem + \\emph{}   \n",
       "9042                 /home/shufan/que_tex/1505.01379.tex    theorem + \\emph{}   \n",
       "9043                 /home/shufan/que_tex/1505.01379.tex    theorem + \\emph{}   \n",
       "9534             /home/shufan/que_tex/SL2Plethysms8+.tex    theorem + \\emph{}   \n",
       "9535             /home/shufan/que_tex/SL2Plethysms8+.tex    theorem + \\emph{}   \n",
       "9976                  /home/shufan/que_tex/1007.3120.tex    theorem + \\emph{}   \n",
       "11305                 /home/shufan/que_tex/1304.7039.tex    theorem + \\emph{}   \n",
       "12213                 /home/shufan/que_tex/0711.3050.tex  theorem + \\textit{}   \n",
       "14243  /home/shufan/que_tex/edgeworth_random_trees-4.tex    theorem + \\emph{}   \n",
       "14244  /home/shufan/que_tex/edgeworth_random_trees-4.tex    theorem + \\emph{}   \n",
       "14245  /home/shufan/que_tex/edgeworth_random_trees-4.tex    theorem + \\emph{}   \n",
       "14531  /home/shufan/que_tex/SubdivisionCDdecompositio...    theorem + \\emph{}   \n",
       "14536  /home/shufan/que_tex/SubdivisionCDdecompositio...    theorem + \\emph{}   \n",
       "14537  /home/shufan/que_tex/SubdivisionCDdecompositio...    theorem + \\emph{}   \n",
       "\n",
       "                                          plain_text_def  \\\n",
       "192    \\nThe association scheme extension algorithm w...   \n",
       "293    Let (n) denote the poset of ordered integer pa...   \n",
       "803    [Kriesell <cit.>] \\n  A graph is a minimal cri...   \n",
       "3140   \\nSuppose x∈(0,1) is fixed. Then:\\n\\n(a) if 0<...   \n",
       "4245    \\n (a) Let μ⊢ n, where n=2k+1. Then\\n  \\n    ...   \n",
       "4246    \\n(a) If n is odd then\\n  \\n    b(n) = b^∗(n)...   \n",
       "7355   \\nLet k≥ 3. There exists  0<ϵ_q=o_q(1) and pos...   \n",
       "8059   \\n\\n\\n\\n\\n  (a) τ_m^∞(P_1 P_n)=n-1.\\n\\n\\n\\n   ...   \n",
       "9041   (Furstenberg)\\n\\nLet κ be a field of positive ...   \n",
       "9042   (Furstenberg)\\n\\nLet 𝔽_q be a finite field of ...   \n",
       "9043   (Christol)\\n\\nLet 𝔽_q be a finite field of cha...   \n",
       "9534   \\nLet  and  be partitions and let ℓ≥ℓ(λ), ℓ(μ)...   \n",
       "9535   \\nLet λ and μ be partitions and let ℓ, m ∈ be ...   \n",
       "9976   \\nhickman\\nThe system\\nℋ = {(H1) , (H2) , (H4)...   \n",
       "11305  \\n\\n\\n  (a) The standard bitableaux are a K-ve...   \n",
       "12213  (Rado)\\nA system of linear equations is regula...   \n",
       "14243  \\nLet (_n(k))_k∈ be the  external profile of a...   \n",
       "14244  \\nConsider a one-split BRW with deterministic ...   \n",
       "14245  \\nLet (_n(k))_k∈ be the profile of a random bi...   \n",
       "14531  \\n(Stanley) <cit.> Let Ω be an S-shellable reg...   \n",
       "14536   (Stanley)Let P be the face poset of a rationa...   \n",
       "14537   (Stanley) Let P be a rational d-polytope. Sup...   \n",
       "\n",
       "                               plain_text_term  \\\n",
       "192                           (P2), (P3), (P4)   \n",
       "293                                        (n)   \n",
       "803                              (TB);(i);(ii)   \n",
       "3140                               (a);(b);(c)   \n",
       "4245                                   (a);(b)   \n",
       "4246                           (a);(b);(c);(d)   \n",
       "7355                          (a);(i);(ii);(b)   \n",
       "8059                                   (b);(c)   \n",
       "9041                             (Furstenberg)   \n",
       "9042                             (Furstenberg)   \n",
       "9043                                (Christol)   \n",
       "9534                                   (a);(b)   \n",
       "9535                               (d);(e);(g)   \n",
       "9976   (H1);(H2);(H4);(H7);(H8);(H3);(H5);(H6)   \n",
       "11305                                      (b)   \n",
       "12213                                   (Rado)   \n",
       "14243                              (a);(b);(c)   \n",
       "14244                              (a);(b);(c)   \n",
       "14245                          (a);(b);(b);(c)   \n",
       "14531                                (Stanley)   \n",
       "14536                                (Stanley)   \n",
       "14537                                (Stanley)   \n",
       "\n",
       "                                   masked_plain_text_def  \\\n",
       "192    \\nThe association scheme extension algorithm w...   \n",
       "293    Let (n) denote the poset of ordered integer pa...   \n",
       "803    [Kriesell <cit.>] \\n  A graph is a minimal cri...   \n",
       "3140   \\nSuppose x∈(0,1) is fixed. Then:\\n\\nB_MATH_TE...   \n",
       "4245    \\n B_MATH_TERM Let μ⊢ n, where n=2k+1. Then\\n...   \n",
       "4246    \\nB_MATH_TERM If n is odd then\\n  \\n    b(n) ...   \n",
       "7355   \\nLet k≥ 3. There exists  0<ϵ_q=o_q(1) and pos...   \n",
       "8059   \\n\\n\\n\\n\\n  (a) τ_m^∞(P_1 P_n)=n-1.\\n\\n\\n\\n   ...   \n",
       "9041   B_MATH_TERM\\n\\nLet κ be a field of positive ch...   \n",
       "9042   B_MATH_TERM\\n\\nLet 𝔽_q be a finite field of ch...   \n",
       "9043   B_MATH_TERM\\n\\nLet 𝔽_q be a finite field of ch...   \n",
       "9534   \\nLet  and  be partitions and let ℓ≥ℓ(λ), ℓ(μ)...   \n",
       "9535   \\nLet λ and μ be partitions and let ℓ, m ∈ be ...   \n",
       "9976   \\nhickman\\nThe system\\nℋ = {B_MATH_TERM , B_MA...   \n",
       "11305  \\n\\n\\n  (a) The standard bitableaux are a K-ve...   \n",
       "12213  B_MATH_TERM\\nA system of linear equations is r...   \n",
       "14243  \\nLet (_n(k))_k∈ be the  external profile of a...   \n",
       "14244  \\nConsider a one-split BRW with deterministic ...   \n",
       "14245  \\nLet (_n(k))_k∈ be the profile of a random bi...   \n",
       "14531  \\nB_MATH_TERM <cit.> Let Ω be an S-shellable r...   \n",
       "14536   B_MATH_TERMLet P be the face poset of a ratio...   \n",
       "14537   B_MATH_TERM Let P be a rational d-polytope. S...   \n",
       "\n",
       "                                             labeled_def  \n",
       "192    O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "293    O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "803    O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "3140   O O O O O B_MATH_TERM O O O O O O O O O O B_MA...  \n",
       "4245   B_MATH_TERM O O O O O O O O O O O O O O O O O ...  \n",
       "4246   B_MATH_TERM O O O O O O O O O O O B_MATH_TERM ...  \n",
       "7355   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "8059   O O O B_MATH_TERM O O O O O O O O O B_MATH_TER...  \n",
       "9041   B_MATH_TERM O O O O O O O O O O O O O O O O O ...  \n",
       "9042   B_MATH_TERM O O O O O O O O O O O O O O O O O ...  \n",
       "9043   B_MATH_TERM O O O O O O O O O O O O O O O O O ...  \n",
       "9534   O O O O O O O O B_MATH_TERM O O O O O O O O O ...  \n",
       "9535   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "9976   O O O O O O O B_MATH_TERM O B_MATH_TERM O B_MA...  \n",
       "11305  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "12213  B_MATH_TERM O O O O O O O O O O O O O O O O O ...  \n",
       "14243  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "14244  O O O O O O O O O O O O O O O O O O O B_MATH_T...  \n",
       "14245  O O O O O O O O O O O O O O O O O O O O O B_MA...  \n",
       "14531  B_MATH_TERM O O O O O O O O O O O O O O O O O ...  \n",
       "14536  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "14537  B_MATH_TERM O O O O O O O O O O O O O O O O O ...  "
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# (1) (i) (TB)\n",
    "df_clean[df_clean['plain_text_term'].str.match(r'^\\s*(\\([A-Za-z0-9]+\\)\\s*([,;]\\s*\\([A-Za-z0-9]+\\)\\s*)*)$')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "b3ca3deb-16e0-40ce-b0d7-a406cf6f23af",
   "metadata": {},
   "outputs": [],
   "source": [
    "# (1) (i) (TB)\n",
    "df_clean = df_clean[ ~df_clean['plain_text_term'].str.match(r'^\\s*(\\([A-Za-z0-9]+\\)\\s*([,;]\\s*\\([A-Za-z0-9]+\\)\\s*)*)$')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "b20e1961-cf93-4858-a9cf-9aaa35ed4a8c",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean.to_csv('cleaned_plain-text_term+combined-term_def_labeled.csv',index=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "adfc4679-af9f-4135-bf3d-367317c14d08",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>term</th>\n",
       "      <th>def</th>\n",
       "      <th>file_name</th>\n",
       "      <th>extraction_rule</th>\n",
       "      <th>plain_text_def</th>\n",
       "      <th>plain_text_term</th>\n",
       "      <th>masked_plain_text_def</th>\n",
       "      <th>labeled_def</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>\\textbf{(Guth, Katz, \\cite[Theorem 4.1]{Guth_K...</td>\n",
       "      <td>\\emph{\\textbf{(Guth, Katz, \\cite[Theorem 4.1]{...</td>\n",
       "      <td>/home/shufan/que_tex/1408.5867.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>(Guth, Katz, &lt;cit.&gt; ) Let 𝔊 be a finite set of...</td>\n",
       "      <td>(Guth, Katz, &lt;cit.&gt;</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM I_MATH_TERM I_MATH_TER...</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM I_MATH_TERM I_MATH_TER...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>592</th>\n",
       "      <td>\\cite[Tab.\\,3]{BDFKMP-ArXiv2015Greedy;2;A.;(i)...</td>\n",
       "      <td>\\label{th1_main}\\nLet $t_{2}(2,q)$ be the smal...</td>\n",
       "      <td>/home/shufan/que_tex/BDFKMP_TabSmallArcFOP4300...</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet t_2(2,q) be the smallest size of a compl...</td>\n",
       "      <td>&lt;cit.&gt;</td>\n",
       "      <td>\\nLet t_2(2,q) be the smallest size of a compl...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>891</th>\n",
       "      <td>(\\cite[Theorem~3.1]{KRS</td>\n",
       "      <td>\\emph{(\\cite[Theorem~3.1]{KRS} )}\\label{THkrse...</td>\n",
       "      <td>/home/shufan/que_tex/1512.06393.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>(&lt;cit.&gt; )\\nLet G be a graph with |L(G)|=1 and ...</td>\n",
       "      <td>(&lt;cit.&gt;</td>\n",
       "      <td>B_MATH_TERM )\\nLet G be a graph with |L(G)|=1 ...</td>\n",
       "      <td>B_MATH_TERM O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>893</th>\n",
       "      <td>\\cite[Sec.\\thinspace 4]{Gropp-nk;0,1-matrix</td>\n",
       "      <td>\\n\\label{Th1_2L+1}\\emph{\\cite[Sec.\\thinspace 4...</td>\n",
       "      <td>/home/shufan/que_tex/1203.0709.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n&lt;cit.&gt;\\n\\n\\n\\n  (i) Any Golomb ruler G_k of ...</td>\n",
       "      <td>&lt;cit.&gt;</td>\n",
       "      <td>\\nB_MATH_TERM I_MATH_TERM\\n\\n\\n\\n  (i) Any Gol...</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2287</th>\n",
       "      <td>\\textbf{(Guth, Katz, \\cite[Theorem 4.1]{Guth_K...</td>\n",
       "      <td>\\emph{\\textbf{(Guth, Katz, \\cite[Theorem 4.1]{...</td>\n",
       "      <td>/home/shufan/que_tex/1203.3735.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>(Guth, Katz, &lt;cit.&gt; ) Let 𝔊 be a finite set of...</td>\n",
       "      <td>(Guth, Katz, &lt;cit.&gt;</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM I_MATH_TERM I_MATH_TER...</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM I_MATH_TERM I_MATH_TER...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2288</th>\n",
       "      <td>\\textbf{(Guth, Katz, \\cite[Corollary 2.5]{Guth...</td>\n",
       "      <td>\\emph{\\textbf{(Guth, Katz, \\cite[Corollary 2.5...</td>\n",
       "      <td>/home/shufan/que_tex/1203.3735.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>(Guth, Katz, &lt;cit.&gt; ) (Corollary of Bézout's T...</td>\n",
       "      <td>(Guth, Katz, &lt;cit.&gt;</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM I_MATH_TERM I_MATH_TER...</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM I_MATH_TERM I_MATH_TER...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2498</th>\n",
       "      <td>\\cite[Theorem 1]{eseq06</td>\n",
       "      <td>\\emph{\\cite[Theorem 1]{eseq06}}\\label{charact...</td>\n",
       "      <td>/home/shufan/que_tex/lagrange.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>&lt;cit.&gt;\\n   A permutation π on [n] is 35241-av...</td>\n",
       "      <td>&lt;cit.&gt;</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM\\n   A permutation π o...</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2908</th>\n",
       "      <td>(\\cite[Theorem 1.1]{ca</td>\n",
       "      <td>\\emph{(\\cite[Theorem 1.1]{ca} ).}\\n\\label{thca...</td>\n",
       "      <td>/home/shufan/que_tex/new.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>(&lt;cit.&gt; ).\\n The poset (S_n) is homotopy Cohen...</td>\n",
       "      <td>(&lt;cit.&gt;</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM ).\\n The poset (S_n) i...</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2909</th>\n",
       "      <td>(\\cite[Theorem 1.2]{ca</td>\n",
       "      <td>\\emph{(\\cite[Theorem 1.2]{ca} ).}\\n\\label{thca...</td>\n",
       "      <td>/home/shufan/que_tex/new.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>(&lt;cit.&gt; ).\\n\\nLet P̅_n=(S_n){e}. The reduced E...</td>\n",
       "      <td>(&lt;cit.&gt;</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM ).\\n\\nLet P̅_n=(S_n){e...</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3689</th>\n",
       "      <td>\\cite[Corollary 9.7]{Q</td>\n",
       "      <td>\\emph{\\cite[Corollary 9.7]{Q}}\\n\\label{Quille...</td>\n",
       "      <td>/home/shufan/que_tex/new_full.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>&lt;cit.&gt;\\n\\n Let P and Q be graded posets. Let ...</td>\n",
       "      <td>&lt;cit.&gt;</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM\\n\\n Let P and Q be gr...</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3743</th>\n",
       "      <td>\\cite[Cor. 3.7.4]{Sti</td>\n",
       "      <td>\\label{Th_Kummer}\\emph{\\cite[Cor. 3.7.4]{Sti}}...</td>\n",
       "      <td>/home/shufan/que_tex/1804.01305.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>&lt;cit.&gt;\\nConsider an algebraic function field  ...</td>\n",
       "      <td>&lt;cit.&gt;</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM\\nConsider an algebraic...</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3744</th>\n",
       "      <td>(Hasse-Weil bound, \\cite[Theorem 5.2.3]{Sti</td>\n",
       "      <td>\\label{HasseWeil}\\emph{(Hasse-Weil bound, \\ci...</td>\n",
       "      <td>/home/shufan/que_tex/1804.01305.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>(Hasse-Weil bound, &lt;cit.&gt; )\\nThe number N_q o...</td>\n",
       "      <td>(Hasse-Weil bound, &lt;cit.&gt;</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM I_MATH_TERM I_MATH_TE...</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM I_MATH_TERM I_MATH_TER...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4028</th>\n",
       "      <td>\\cite[p.199]{cp</td>\n",
       "      <td>\\emph{\\cite[p.199]{cp}}\\label{T:UhPBW}\\n  The ...</td>\n",
       "      <td>/home/shufan/que_tex/HolfAlgSTR12.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>&lt;cit.&gt;\\n  The set _h {^̋r^s^t : a,b,c ∈_≥ 0} i...</td>\n",
       "      <td>&lt;cit.&gt;</td>\n",
       "      <td>B_MATH_TERM\\n  The set _h {^̋r^s^t : a,b,c ∈_≥...</td>\n",
       "      <td>B_MATH_TERM O O O O O O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6442</th>\n",
       "      <td>\\cite[Theorem 1.1]{BG</td>\n",
       "      <td>\\n\\label{th:BG}\\n\\emph{\\cite[Theorem 1.1]{BG}}...</td>\n",
       "      <td>/home/shufan/que_tex/1409.1314.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n\\n&lt;cit.&gt; \\nLet r≥ 3 be a fixed integer. \\nLe...</td>\n",
       "      <td>&lt;cit.&gt;</td>\n",
       "      <td>\\n\\nB_MATH_TERM I_MATH_TERM \\nLet r≥ 3 be a fi...</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7370</th>\n",
       "      <td>\\cite[Theorem 27.5.1 (v)]{JWPH3</td>\n",
       "      <td>\\label{t:HT}\\emph{\\cite[Theorem 27.5.1 (v)]{JW...</td>\n",
       "      <td>/home/shufan/que_tex/1506.08875.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>&lt;cit.&gt;\\n  Let q≥ t+1.\\n  Then there is a uniqu...</td>\n",
       "      <td>&lt;cit.&gt;</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM I_MATH_TERM\\n  Let q≥ ...</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM I_MATH_TERM O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8569</th>\n",
       "      <td>\\cite[Theorem 2.4]{TV</td>\n",
       "      <td>\\emph{\\cite[Theorem 2.4]{TV}} \\label{renyi}\\n ...</td>\n",
       "      <td>/home/shufan/que_tex/1701.08101.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>&lt;cit.&gt; \\n The cardinality of each vertex part ...</td>\n",
       "      <td>&lt;cit.&gt;</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM \\n The cardinality of ...</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9029</th>\n",
       "      <td>(\\cite[Theorem~22]{CW2005</td>\n",
       "      <td>\\label{thm1}\\n\\emph{(\\cite[Theorem~22]{CW2005}...</td>\n",
       "      <td>/home/shufan/que_tex/1702.04559.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n(&lt;cit.&gt; ) If q≢16, then\\n\\n    (_2(q))=\\n   ...</td>\n",
       "      <td>(&lt;cit.&gt;</td>\n",
       "      <td>\\nB_MATH_TERM ) If q≢16, then\\n\\n    (_2(q))=\\...</td>\n",
       "      <td>B_MATH_TERM O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9807</th>\n",
       "      <td>\\cite[Theorems~3.126\\&amp;5.89]{orlikterao</td>\n",
       "      <td>\\n\\label{orliksolomonalgebra}\\n\\emph{\\cite[The...</td>\n",
       "      <td>/home/shufan/que_tex/qldrhtca.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n\\n&lt;cit.&gt;\\nLet Γ=(,) be an ordered graph, and...</td>\n",
       "      <td>&lt;cit.&gt;</td>\n",
       "      <td>\\n\\nB_MATH_TERM\\nLet Γ=(,) be an ordered graph...</td>\n",
       "      <td>B_MATH_TERM O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9808</th>\n",
       "      <td>\\cite[Theorem~5.2]{deconciniprocesi</td>\n",
       "      <td>\\n\\label{toriccohomology}\\n\\emph{\\cite[Theorem...</td>\n",
       "      <td>/home/shufan/que_tex/qldrhtca.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n\\n&lt;cit.&gt;\\nLet Γ=(,) be an ordered graph, and...</td>\n",
       "      <td>&lt;cit.&gt;</td>\n",
       "      <td>\\n\\nB_MATH_TERM\\nLet Γ=(,) be an ordered graph...</td>\n",
       "      <td>B_MATH_TERM O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9809</th>\n",
       "      <td>\\cite[Theorem~12.8]{bousfield</td>\n",
       "      <td>\\emph{\\cite[Theorem~12.8]{bousfield}} \\label{...</td>\n",
       "      <td>/home/shufan/que_tex/qldrhtca.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>&lt;cit.&gt; \\nThere are natural bijections \\n    π...</td>\n",
       "      <td>&lt;cit.&gt;</td>\n",
       "      <td>B_MATH_TERM \\nThere are natural bijections \\n...</td>\n",
       "      <td>B_MATH_TERM O O O O O O O O O O O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9810</th>\n",
       "      <td>\\cite[Theorem~12.8]{bousfield</td>\n",
       "      <td>\\emph{\\cite[Theorem~12.8]{bousfield}}\\nLet $(...</td>\n",
       "      <td>/home/shufan/que_tex/qldrhtca.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>&lt;cit.&gt;\\nLet (M(X),d) be the minimal model of ...</td>\n",
       "      <td>&lt;cit.&gt;</td>\n",
       "      <td>B_MATH_TERM\\nLet (M(X),d) be the minimal mode...</td>\n",
       "      <td>B_MATH_TERM O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9811</th>\n",
       "      <td>\\cite[Theorem~13.2]{griffithsmorgan</td>\n",
       "      <td>\\emph{\\cite[Theorem~13.2]{griffithsmorgan}}\\n...</td>\n",
       "      <td>/home/shufan/que_tex/qldrhtca.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>&lt;cit.&gt;\\nThere are natural isomorphisms \\n    ...</td>\n",
       "      <td>&lt;cit.&gt;</td>\n",
       "      <td>B_MATH_TERM\\nThere are natural isomorphisms \\...</td>\n",
       "      <td>B_MATH_TERM O O O O O O O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10593</th>\n",
       "      <td>\\cite[Theorem 20]{EllisFP11</td>\n",
       "      <td>\\emph{\\cite[Theorem 20]{EllisFP11}}\\nThe $F \\t...</td>\n",
       "      <td>/home/shufan/que_tex/t-matchings-final.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>&lt;cit.&gt;\\nThe F × F leading principal minor of t...</td>\n",
       "      <td>&lt;cit.&gt;</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM\\nThe F × F leading pri...</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11711</th>\n",
       "      <td>semiregular;\\cite[p. 77]{martini</td>\n",
       "      <td>An abstract polytope $\\Po$ is \\emph{semiregul...</td>\n",
       "      <td>/home/shufan/que_tex/revised_Monson-Schulte.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>An abstract polytope  is semiregular\\nif it h...</td>\n",
       "      <td>semiregular;&lt;cit.&gt;</td>\n",
       "      <td>An abstract polytope  is B_MATH_TERM\\nif it h...</td>\n",
       "      <td>O O O O B_MATH_TERM O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11753</th>\n",
       "      <td>(~\\cite[Theorem 1]{DFRS</td>\n",
       "      <td>\\emph{(~\\cite[Theorem 1]{DFRS} )}\\\\nFor each ...</td>\n",
       "      <td>/home/shufan/que_tex/BG-revision.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>( &lt;cit.&gt; )For each integer r≥ 3, define \\n\\n ...</td>\n",
       "      <td>( &lt;cit.&gt;</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM )For each integer r≥ ...</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12466</th>\n",
       "      <td>\\cite[Theorem 4.8]{tree_structure</td>\n",
       "      <td>\\label{tree_from_N}\\n    \\emph{\\cite[Theorem 4...</td>\n",
       "      <td>/home/shufan/que_tex/separableBlocks.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n    &lt;cit.&gt;\\n    Let N be a canonical nested ...</td>\n",
       "      <td>&lt;cit.&gt;</td>\n",
       "      <td>\\n    B_MATH_TERM I_MATH_TERM\\n    Let N be a ...</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12467</th>\n",
       "      <td>\\cite[Theorem~2.6]{profiles</td>\n",
       "      <td>\\label{canon_td_profiles} %TODO profile of ord...</td>\n",
       "      <td>/home/shufan/que_tex/separableBlocks.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n    &lt;cit.&gt;[Since &lt;cit.&gt; is unpublished, see...</td>\n",
       "      <td>&lt;cit.&gt;</td>\n",
       "      <td>\\n    B_MATH_TERM[Since &lt;cit.&gt; is unpublished...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12648</th>\n",
       "      <td>(\\cite[Theorem~1.4]{Zhang:rigidity</td>\n",
       "      <td>\\n\\emph{(\\cite[Theorem~1.4]{Zhang:rigidity} )}...</td>\n",
       "      <td>/home/shufan/que_tex/lifting_arxiv.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n(&lt;cit.&gt; )\\n\\nIf 𝐀 varies smoothly in M^d and...</td>\n",
       "      <td>(&lt;cit.&gt;</td>\n",
       "      <td>\\nB_MATH_TERM )\\n\\nIf 𝐀 varies smoothly in M^d...</td>\n",
       "      <td>B_MATH_TERM O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12649</th>\n",
       "      <td>(\\cite[Theorem~2.13]{Zhang:rigidity</td>\n",
       "      <td>\\n\\emph{(\\cite[Theorem~2.13]{Zhang:rigidity} )...</td>\n",
       "      <td>/home/shufan/que_tex/lifting_arxiv.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n(&lt;cit.&gt; )\\n\\nLet K be a cell complex in M^d ...</td>\n",
       "      <td>(&lt;cit.&gt;</td>\n",
       "      <td>\\nB_MATH_TERM )\\n\\nLet K be a cell complex in ...</td>\n",
       "      <td>B_MATH_TERM O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13307</th>\n",
       "      <td>(\\cite[Theorem 19.2.8]{DL97;(1);(2);(3)</td>\n",
       "      <td>\\emph{(\\cite[Theorem 19.2.8]{DL97} , \\cite{GW8...</td>\n",
       "      <td>/home/shufan/que_tex/1512.04160.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>(&lt;cit.&gt; , &lt;cit.&gt; and &lt;cit.&gt;)\\nLet Γ be a conne...</td>\n",
       "      <td>(&lt;cit.&gt;</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM , &lt;cit.&gt; and &lt;cit.&gt;)\\n...</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13546</th>\n",
       "      <td>\\cite[Theorem 2.2.19]{ARCHER14</td>\n",
       "      <td>\\emph{\\cite[Theorem 2.2.19]{ARCHER14}}\\label{B...</td>\n",
       "      <td>/home/shufan/que_tex/cyclicperm3by1gridclass_a...</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>&lt;cit.&gt;\\nFor k ≥ 2, n ≥3 and σ∈{+,-}^k,\\n\\t\\n  ...</td>\n",
       "      <td>&lt;cit.&gt;</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM\\nFor k ≥ 2, n ≥3 and σ...</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13897</th>\n",
       "      <td>\\cite[Theorem~7.5]{biggs</td>\n",
       "      <td>\\label{component} \\emph{\\cite[Theorem~7.5]{big...</td>\n",
       "      <td>/home/shufan/que_tex/1909.06578.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>&lt;cit.&gt;\\nThe Laplacian coefficient ξ_n-k of a ...</td>\n",
       "      <td>&lt;cit.&gt;</td>\n",
       "      <td>B_MATH_TERM\\nThe Laplacian coefficient ξ_n-k ...</td>\n",
       "      <td>B_MATH_TERM O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13898</th>\n",
       "      <td>\\cite[Theorem 3.2]{mohar</td>\n",
       "      <td>\\label{eqution} \\emph{\\cite[Theorem 3.2]{mohar...</td>\n",
       "      <td>/home/shufan/que_tex/1909.06578.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>&lt;cit.&gt;\\nLet G be a graph on n vertices and e ...</td>\n",
       "      <td>&lt;cit.&gt;</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM\\nLet G be a graph on ...</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14837</th>\n",
       "      <td>(\\cite[1.9]{Reid;can;:\\smallskip;(i);can;(;);(...</td>\n",
       "      <td>\\label{WAHLREID}\\t\\emph{(\\cite[1.9]{Reid} , \\c...</td>\n",
       "      <td>/home/shufan/que_tex/Twelveptthm.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\t(&lt;cit.&gt; , &lt;cit.&gt; and &lt;cit.&gt;)\\nThe pair (U^ca...</td>\n",
       "      <td>(&lt;cit.&gt;</td>\n",
       "      <td>\\tB_MATH_TERM , &lt;cit.&gt; and &lt;cit.&gt;)\\nThe pair (...</td>\n",
       "      <td>B_MATH_TERM O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                    term  \\\n",
       "98     \\textbf{(Guth, Katz, \\cite[Theorem 4.1]{Guth_K...   \n",
       "592    \\cite[Tab.\\,3]{BDFKMP-ArXiv2015Greedy;2;A.;(i)...   \n",
       "891                              (\\cite[Theorem~3.1]{KRS   \n",
       "893          \\cite[Sec.\\thinspace 4]{Gropp-nk;0,1-matrix   \n",
       "2287   \\textbf{(Guth, Katz, \\cite[Theorem 4.1]{Guth_K...   \n",
       "2288   \\textbf{(Guth, Katz, \\cite[Corollary 2.5]{Guth...   \n",
       "2498                             \\cite[Theorem 1]{eseq06   \n",
       "2908                              (\\cite[Theorem 1.1]{ca   \n",
       "2909                              (\\cite[Theorem 1.2]{ca   \n",
       "3689                              \\cite[Corollary 9.7]{Q   \n",
       "3743                               \\cite[Cor. 3.7.4]{Sti   \n",
       "3744         (Hasse-Weil bound, \\cite[Theorem 5.2.3]{Sti   \n",
       "4028                                     \\cite[p.199]{cp   \n",
       "6442                               \\cite[Theorem 1.1]{BG   \n",
       "7370                     \\cite[Theorem 27.5.1 (v)]{JWPH3   \n",
       "8569                               \\cite[Theorem 2.4]{TV   \n",
       "9029                           (\\cite[Theorem~22]{CW2005   \n",
       "9807              \\cite[Theorems~3.126\\&5.89]{orlikterao   \n",
       "9808                 \\cite[Theorem~5.2]{deconciniprocesi   \n",
       "9809                       \\cite[Theorem~12.8]{bousfield   \n",
       "9810                       \\cite[Theorem~12.8]{bousfield   \n",
       "9811                 \\cite[Theorem~13.2]{griffithsmorgan   \n",
       "10593                        \\cite[Theorem 20]{EllisFP11   \n",
       "11711                   semiregular;\\cite[p. 77]{martini   \n",
       "11753                            (~\\cite[Theorem 1]{DFRS   \n",
       "12466                  \\cite[Theorem 4.8]{tree_structure   \n",
       "12467                        \\cite[Theorem~2.6]{profiles   \n",
       "12648                 (\\cite[Theorem~1.4]{Zhang:rigidity   \n",
       "12649                (\\cite[Theorem~2.13]{Zhang:rigidity   \n",
       "13307            (\\cite[Theorem 19.2.8]{DL97;(1);(2);(3)   \n",
       "13546                     \\cite[Theorem 2.2.19]{ARCHER14   \n",
       "13897                           \\cite[Theorem~7.5]{biggs   \n",
       "13898                           \\cite[Theorem 3.2]{mohar   \n",
       "14837  (\\cite[1.9]{Reid;can;:\\smallskip;(i);can;(;);(...   \n",
       "\n",
       "                                                     def  \\\n",
       "98     \\emph{\\textbf{(Guth, Katz, \\cite[Theorem 4.1]{...   \n",
       "592    \\label{th1_main}\\nLet $t_{2}(2,q)$ be the smal...   \n",
       "891    \\emph{(\\cite[Theorem~3.1]{KRS} )}\\label{THkrse...   \n",
       "893    \\n\\label{Th1_2L+1}\\emph{\\cite[Sec.\\thinspace 4...   \n",
       "2287   \\emph{\\textbf{(Guth, Katz, \\cite[Theorem 4.1]{...   \n",
       "2288   \\emph{\\textbf{(Guth, Katz, \\cite[Corollary 2.5...   \n",
       "2498    \\emph{\\cite[Theorem 1]{eseq06}}\\label{charact...   \n",
       "2908   \\emph{(\\cite[Theorem 1.1]{ca} ).}\\n\\label{thca...   \n",
       "2909   \\emph{(\\cite[Theorem 1.2]{ca} ).}\\n\\label{thca...   \n",
       "3689    \\emph{\\cite[Corollary 9.7]{Q}}\\n\\label{Quille...   \n",
       "3743   \\label{Th_Kummer}\\emph{\\cite[Cor. 3.7.4]{Sti}}...   \n",
       "3744    \\label{HasseWeil}\\emph{(Hasse-Weil bound, \\ci...   \n",
       "4028   \\emph{\\cite[p.199]{cp}}\\label{T:UhPBW}\\n  The ...   \n",
       "6442   \\n\\label{th:BG}\\n\\emph{\\cite[Theorem 1.1]{BG}}...   \n",
       "7370   \\label{t:HT}\\emph{\\cite[Theorem 27.5.1 (v)]{JW...   \n",
       "8569   \\emph{\\cite[Theorem 2.4]{TV}} \\label{renyi}\\n ...   \n",
       "9029   \\label{thm1}\\n\\emph{(\\cite[Theorem~22]{CW2005}...   \n",
       "9807   \\n\\label{orliksolomonalgebra}\\n\\emph{\\cite[The...   \n",
       "9808   \\n\\label{toriccohomology}\\n\\emph{\\cite[Theorem...   \n",
       "9809    \\emph{\\cite[Theorem~12.8]{bousfield}} \\label{...   \n",
       "9810    \\emph{\\cite[Theorem~12.8]{bousfield}}\\nLet $(...   \n",
       "9811    \\emph{\\cite[Theorem~13.2]{griffithsmorgan}}\\n...   \n",
       "10593  \\emph{\\cite[Theorem 20]{EllisFP11}}\\nThe $F \\t...   \n",
       "11711   An abstract polytope $\\Po$ is \\emph{semiregul...   \n",
       "11753   \\emph{(~\\cite[Theorem 1]{DFRS} )}\\\\nFor each ...   \n",
       "12466  \\label{tree_from_N}\\n    \\emph{\\cite[Theorem 4...   \n",
       "12467  \\label{canon_td_profiles} %TODO profile of ord...   \n",
       "12648  \\n\\emph{(\\cite[Theorem~1.4]{Zhang:rigidity} )}...   \n",
       "12649  \\n\\emph{(\\cite[Theorem~2.13]{Zhang:rigidity} )...   \n",
       "13307  \\emph{(\\cite[Theorem 19.2.8]{DL97} , \\cite{GW8...   \n",
       "13546  \\emph{\\cite[Theorem 2.2.19]{ARCHER14}}\\label{B...   \n",
       "13897  \\label{component} \\emph{\\cite[Theorem~7.5]{big...   \n",
       "13898  \\label{eqution} \\emph{\\cite[Theorem 3.2]{mohar...   \n",
       "14837  \\label{WAHLREID}\\t\\emph{(\\cite[1.9]{Reid} , \\c...   \n",
       "\n",
       "                                               file_name  \\\n",
       "98                    /home/shufan/que_tex/1408.5867.tex   \n",
       "592    /home/shufan/que_tex/BDFKMP_TabSmallArcFOP4300...   \n",
       "891                  /home/shufan/que_tex/1512.06393.tex   \n",
       "893                   /home/shufan/que_tex/1203.0709.tex   \n",
       "2287                  /home/shufan/que_tex/1203.3735.tex   \n",
       "2288                  /home/shufan/que_tex/1203.3735.tex   \n",
       "2498                   /home/shufan/que_tex/lagrange.tex   \n",
       "2908                        /home/shufan/que_tex/new.tex   \n",
       "2909                        /home/shufan/que_tex/new.tex   \n",
       "3689                   /home/shufan/que_tex/new_full.tex   \n",
       "3743                 /home/shufan/que_tex/1804.01305.tex   \n",
       "3744                 /home/shufan/que_tex/1804.01305.tex   \n",
       "4028               /home/shufan/que_tex/HolfAlgSTR12.tex   \n",
       "6442                  /home/shufan/que_tex/1409.1314.tex   \n",
       "7370                 /home/shufan/que_tex/1506.08875.tex   \n",
       "8569                 /home/shufan/que_tex/1701.08101.tex   \n",
       "9029                 /home/shufan/que_tex/1702.04559.tex   \n",
       "9807                   /home/shufan/que_tex/qldrhtca.tex   \n",
       "9808                   /home/shufan/que_tex/qldrhtca.tex   \n",
       "9809                   /home/shufan/que_tex/qldrhtca.tex   \n",
       "9810                   /home/shufan/que_tex/qldrhtca.tex   \n",
       "9811                   /home/shufan/que_tex/qldrhtca.tex   \n",
       "10593         /home/shufan/que_tex/t-matchings-final.tex   \n",
       "11711    /home/shufan/que_tex/revised_Monson-Schulte.tex   \n",
       "11753               /home/shufan/que_tex/BG-revision.tex   \n",
       "12466           /home/shufan/que_tex/separableBlocks.tex   \n",
       "12467           /home/shufan/que_tex/separableBlocks.tex   \n",
       "12648             /home/shufan/que_tex/lifting_arxiv.tex   \n",
       "12649             /home/shufan/que_tex/lifting_arxiv.tex   \n",
       "13307                /home/shufan/que_tex/1512.04160.tex   \n",
       "13546  /home/shufan/que_tex/cyclicperm3by1gridclass_a...   \n",
       "13897                /home/shufan/que_tex/1909.06578.tex   \n",
       "13898                /home/shufan/que_tex/1909.06578.tex   \n",
       "14837               /home/shufan/que_tex/Twelveptthm.tex   \n",
       "\n",
       "            extraction_rule  \\\n",
       "98        theorem + \\emph{}   \n",
       "592       theorem + \\emph{}   \n",
       "891       theorem + \\emph{}   \n",
       "893       theorem + \\emph{}   \n",
       "2287      theorem + \\emph{}   \n",
       "2288      theorem + \\emph{}   \n",
       "2498      theorem + \\emph{}   \n",
       "2908      theorem + \\emph{}   \n",
       "2909      theorem + \\emph{}   \n",
       "3689      theorem + \\emph{}   \n",
       "3743      theorem + \\emph{}   \n",
       "3744      theorem + \\emph{}   \n",
       "4028      theorem + \\emph{}   \n",
       "6442      theorem + \\emph{}   \n",
       "7370      theorem + \\emph{}   \n",
       "8569      theorem + \\emph{}   \n",
       "9029      theorem + \\emph{}   \n",
       "9807      theorem + \\emph{}   \n",
       "9808      theorem + \\emph{}   \n",
       "9809      theorem + \\emph{}   \n",
       "9810      theorem + \\emph{}   \n",
       "9811      theorem + \\emph{}   \n",
       "10593     theorem + \\emph{}   \n",
       "11711  definition + \\emph{}   \n",
       "11753     theorem + \\emph{}   \n",
       "12466     theorem + \\emph{}   \n",
       "12467     theorem + \\emph{}   \n",
       "12648     theorem + \\emph{}   \n",
       "12649     theorem + \\emph{}   \n",
       "13307     theorem + \\emph{}   \n",
       "13546     theorem + \\emph{}   \n",
       "13897     theorem + \\emph{}   \n",
       "13898     theorem + \\emph{}   \n",
       "14837     theorem + \\emph{}   \n",
       "\n",
       "                                          plain_text_def  \\\n",
       "98     (Guth, Katz, <cit.> ) Let 𝔊 be a finite set of...   \n",
       "592    \\nLet t_2(2,q) be the smallest size of a compl...   \n",
       "891    (<cit.> )\\nLet G be a graph with |L(G)|=1 and ...   \n",
       "893    \\n<cit.>\\n\\n\\n\\n  (i) Any Golomb ruler G_k of ...   \n",
       "2287   (Guth, Katz, <cit.> ) Let 𝔊 be a finite set of...   \n",
       "2288   (Guth, Katz, <cit.> ) (Corollary of Bézout's T...   \n",
       "2498    <cit.>\\n   A permutation π on [n] is 35241-av...   \n",
       "2908   (<cit.> ).\\n The poset (S_n) is homotopy Cohen...   \n",
       "2909   (<cit.> ).\\n\\nLet P̅_n=(S_n){e}. The reduced E...   \n",
       "3689    <cit.>\\n\\n Let P and Q be graded posets. Let ...   \n",
       "3743   <cit.>\\nConsider an algebraic function field  ...   \n",
       "3744    (Hasse-Weil bound, <cit.> )\\nThe number N_q o...   \n",
       "4028   <cit.>\\n  The set _h {^̋r^s^t : a,b,c ∈_≥ 0} i...   \n",
       "6442   \\n\\n<cit.> \\nLet r≥ 3 be a fixed integer. \\nLe...   \n",
       "7370   <cit.>\\n  Let q≥ t+1.\\n  Then there is a uniqu...   \n",
       "8569   <cit.> \\n The cardinality of each vertex part ...   \n",
       "9029   \\n(<cit.> ) If q≢16, then\\n\\n    (_2(q))=\\n   ...   \n",
       "9807   \\n\\n<cit.>\\nLet Γ=(,) be an ordered graph, and...   \n",
       "9808   \\n\\n<cit.>\\nLet Γ=(,) be an ordered graph, and...   \n",
       "9809    <cit.> \\nThere are natural bijections \\n    π...   \n",
       "9810    <cit.>\\nLet (M(X),d) be the minimal model of ...   \n",
       "9811    <cit.>\\nThere are natural isomorphisms \\n    ...   \n",
       "10593  <cit.>\\nThe F × F leading principal minor of t...   \n",
       "11711   An abstract polytope  is semiregular\\nif it h...   \n",
       "11753   ( <cit.> )For each integer r≥ 3, define \\n\\n ...   \n",
       "12466  \\n    <cit.>\\n    Let N be a canonical nested ...   \n",
       "12467   \\n    <cit.>[Since <cit.> is unpublished, see...   \n",
       "12648  \\n(<cit.> )\\n\\nIf 𝐀 varies smoothly in M^d and...   \n",
       "12649  \\n(<cit.> )\\n\\nLet K be a cell complex in M^d ...   \n",
       "13307  (<cit.> , <cit.> and <cit.>)\\nLet Γ be a conne...   \n",
       "13546  <cit.>\\nFor k ≥ 2, n ≥3 and σ∈{+,-}^k,\\n\\t\\n  ...   \n",
       "13897   <cit.>\\nThe Laplacian coefficient ξ_n-k of a ...   \n",
       "13898   <cit.>\\nLet G be a graph on n vertices and e ...   \n",
       "14837  \\t(<cit.> , <cit.> and <cit.>)\\nThe pair (U^ca...   \n",
       "\n",
       "                 plain_text_term  \\\n",
       "98           (Guth, Katz, <cit.>   \n",
       "592                       <cit.>   \n",
       "891                      (<cit.>   \n",
       "893                       <cit.>   \n",
       "2287         (Guth, Katz, <cit.>   \n",
       "2288         (Guth, Katz, <cit.>   \n",
       "2498                      <cit.>   \n",
       "2908                     (<cit.>   \n",
       "2909                     (<cit.>   \n",
       "3689                      <cit.>   \n",
       "3743                      <cit.>   \n",
       "3744   (Hasse-Weil bound, <cit.>   \n",
       "4028                      <cit.>   \n",
       "6442                      <cit.>   \n",
       "7370                      <cit.>   \n",
       "8569                      <cit.>   \n",
       "9029                     (<cit.>   \n",
       "9807                      <cit.>   \n",
       "9808                      <cit.>   \n",
       "9809                      <cit.>   \n",
       "9810                      <cit.>   \n",
       "9811                      <cit.>   \n",
       "10593                     <cit.>   \n",
       "11711         semiregular;<cit.>   \n",
       "11753                   ( <cit.>   \n",
       "12466                     <cit.>   \n",
       "12467                     <cit.>   \n",
       "12648                    (<cit.>   \n",
       "12649                    (<cit.>   \n",
       "13307                    (<cit.>   \n",
       "13546                     <cit.>   \n",
       "13897                     <cit.>   \n",
       "13898                     <cit.>   \n",
       "14837                    (<cit.>   \n",
       "\n",
       "                                   masked_plain_text_def  \\\n",
       "98     B_MATH_TERM I_MATH_TERM I_MATH_TERM I_MATH_TER...   \n",
       "592    \\nLet t_2(2,q) be the smallest size of a compl...   \n",
       "891    B_MATH_TERM )\\nLet G be a graph with |L(G)|=1 ...   \n",
       "893    \\nB_MATH_TERM I_MATH_TERM\\n\\n\\n\\n  (i) Any Gol...   \n",
       "2287   B_MATH_TERM I_MATH_TERM I_MATH_TERM I_MATH_TER...   \n",
       "2288   B_MATH_TERM I_MATH_TERM I_MATH_TERM I_MATH_TER...   \n",
       "2498    B_MATH_TERM I_MATH_TERM\\n   A permutation π o...   \n",
       "2908   B_MATH_TERM I_MATH_TERM ).\\n The poset (S_n) i...   \n",
       "2909   B_MATH_TERM I_MATH_TERM ).\\n\\nLet P̅_n=(S_n){e...   \n",
       "3689    B_MATH_TERM I_MATH_TERM\\n\\n Let P and Q be gr...   \n",
       "3743   B_MATH_TERM I_MATH_TERM\\nConsider an algebraic...   \n",
       "3744    B_MATH_TERM I_MATH_TERM I_MATH_TERM I_MATH_TE...   \n",
       "4028   B_MATH_TERM\\n  The set _h {^̋r^s^t : a,b,c ∈_≥...   \n",
       "6442   \\n\\nB_MATH_TERM I_MATH_TERM \\nLet r≥ 3 be a fi...   \n",
       "7370   B_MATH_TERM I_MATH_TERM I_MATH_TERM\\n  Let q≥ ...   \n",
       "8569   B_MATH_TERM I_MATH_TERM \\n The cardinality of ...   \n",
       "9029   \\nB_MATH_TERM ) If q≢16, then\\n\\n    (_2(q))=\\...   \n",
       "9807   \\n\\nB_MATH_TERM\\nLet Γ=(,) be an ordered graph...   \n",
       "9808   \\n\\nB_MATH_TERM\\nLet Γ=(,) be an ordered graph...   \n",
       "9809    B_MATH_TERM \\nThere are natural bijections \\n...   \n",
       "9810    B_MATH_TERM\\nLet (M(X),d) be the minimal mode...   \n",
       "9811    B_MATH_TERM\\nThere are natural isomorphisms \\...   \n",
       "10593  B_MATH_TERM I_MATH_TERM\\nThe F × F leading pri...   \n",
       "11711   An abstract polytope  is B_MATH_TERM\\nif it h...   \n",
       "11753   B_MATH_TERM I_MATH_TERM )For each integer r≥ ...   \n",
       "12466  \\n    B_MATH_TERM I_MATH_TERM\\n    Let N be a ...   \n",
       "12467   \\n    B_MATH_TERM[Since <cit.> is unpublished...   \n",
       "12648  \\nB_MATH_TERM )\\n\\nIf 𝐀 varies smoothly in M^d...   \n",
       "12649  \\nB_MATH_TERM )\\n\\nLet K be a cell complex in ...   \n",
       "13307  B_MATH_TERM I_MATH_TERM , <cit.> and <cit.>)\\n...   \n",
       "13546  B_MATH_TERM I_MATH_TERM\\nFor k ≥ 2, n ≥3 and σ...   \n",
       "13897   B_MATH_TERM\\nThe Laplacian coefficient ξ_n-k ...   \n",
       "13898   B_MATH_TERM I_MATH_TERM\\nLet G be a graph on ...   \n",
       "14837  \\tB_MATH_TERM , <cit.> and <cit.>)\\nThe pair (...   \n",
       "\n",
       "                                             labeled_def  \n",
       "98     B_MATH_TERM I_MATH_TERM I_MATH_TERM I_MATH_TER...  \n",
       "592    O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "891    B_MATH_TERM O O O O O O O O O O O O O O O O O ...  \n",
       "893    B_MATH_TERM I_MATH_TERM O O O O O O O O O O O ...  \n",
       "2287   B_MATH_TERM I_MATH_TERM I_MATH_TERM I_MATH_TER...  \n",
       "2288   B_MATH_TERM I_MATH_TERM I_MATH_TERM I_MATH_TER...  \n",
       "2498   B_MATH_TERM I_MATH_TERM O O O O O O O O O O O ...  \n",
       "2908   B_MATH_TERM I_MATH_TERM O O O O O O O O O O O ...  \n",
       "2909   B_MATH_TERM I_MATH_TERM O O O O O O O O O O O ...  \n",
       "3689   B_MATH_TERM I_MATH_TERM O O O O O O O O O O O ...  \n",
       "3743   B_MATH_TERM I_MATH_TERM O O O O O O O O O O O ...  \n",
       "3744   B_MATH_TERM I_MATH_TERM I_MATH_TERM I_MATH_TER...  \n",
       "4028               B_MATH_TERM O O O O O O O O O O O O O  \n",
       "6442   B_MATH_TERM I_MATH_TERM O O O O O O O O O O O ...  \n",
       "7370   B_MATH_TERM I_MATH_TERM I_MATH_TERM O O O O O ...  \n",
       "8569   B_MATH_TERM I_MATH_TERM O O O O O O O O O O O ...  \n",
       "9029   B_MATH_TERM O O O O O O O O O O O O O O O O O ...  \n",
       "9807   B_MATH_TERM O O O O O O O O O O O O O O O O O ...  \n",
       "9808   B_MATH_TERM O O O O O O O O O O O O O O O O O ...  \n",
       "9809     B_MATH_TERM O O O O O O O O O O O O O O O O O O  \n",
       "9810   B_MATH_TERM O O O O O O O O O O O O O O O O O ...  \n",
       "9811             B_MATH_TERM O O O O O O O O O O O O O O  \n",
       "10593  B_MATH_TERM I_MATH_TERM O O O O O O O O O O O ...  \n",
       "11711  O O O O B_MATH_TERM O O O O O O O O O O O O O ...  \n",
       "11753  B_MATH_TERM I_MATH_TERM O O O O O O O O O O O ...  \n",
       "12466  B_MATH_TERM I_MATH_TERM O O O O O O O O O O O ...  \n",
       "12467  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "12648  B_MATH_TERM O O O O O O O O O O O O O O O O O ...  \n",
       "12649  B_MATH_TERM O O O O O O O O O O O O O O O O O ...  \n",
       "13307  B_MATH_TERM I_MATH_TERM O O O O O O O O O O O ...  \n",
       "13546  B_MATH_TERM I_MATH_TERM O O O O O O O O O O O ...  \n",
       "13897  B_MATH_TERM O O O O O O O O O O O O O O O O O ...  \n",
       "13898  B_MATH_TERM I_MATH_TERM O O O O O O O O O O O ...  \n",
       "14837  B_MATH_TERM O O O O O O O O O O O O O O O O O ...  "
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# citations\n",
    "df_clean[df_clean['plain_text_term'].str.contains('<cit')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "43d4c75e-a073-43b6-9227-df0d15fc28d9",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean = df_clean[~df_clean['plain_text_term'].str.contains('<cit')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "ef9e02fe-35c8-487f-ac6a-079f0d7c3b44",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>term</th>\n",
       "      <th>def</th>\n",
       "      <th>file_name</th>\n",
       "      <th>extraction_rule</th>\n",
       "      <th>plain_text_def</th>\n",
       "      <th>plain_text_term</th>\n",
       "      <th>masked_plain_text_def</th>\n",
       "      <th>labeled_def</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>316</th>\n",
       "      <td>Statement of Theorem \\ref{thm:singleton_b_is_a...</td>\n",
       "      <td>\\n%\\label{thm:singleton_b_is_a_prime}\\n\\emph{S...</td>\n",
       "      <td>/home/shufan/que_tex/1803.03954.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n\\nStatement of Theorem &lt;ref&gt;: Let n be a pos...</td>\n",
       "      <td>Statement of Theorem &lt;ref&gt;</td>\n",
       "      <td>\\n\\nB_MATH_TERM I_MATH_TERM I_MATH_TERM I_MATH...</td>\n",
       "      <td>B_MATH_TERM I_MATH_TERM I_MATH_TERM O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>894</th>\n",
       "      <td>(\\ref{eq3.2_Ah_Bh;\\ref{def3.2_Asigma;circulant...</td>\n",
       "      <td>\\n\\label{th3.2_Asigma-s}Let $(a_{1},a_{2},\\ldo...</td>\n",
       "      <td>/home/shufan/que_tex/1203.0709.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet (a_1,a_2,… ,a_k) be a\\n(v,k) modular Gol...</td>\n",
       "      <td>(&lt;ref&gt;</td>\n",
       "      <td>\\nLet (a_1,a_2,… ,a_k) be a\\n(v,k) modular Gol...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>908</th>\n",
       "      <td>(\\ref{LB_M1_general</td>\n",
       "      <td>\\label{LB_M1_general_theorem}\\nFor $n \\ge 2$\\n...</td>\n",
       "      <td>/home/shufan/que_tex/Goubko.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nFor n ≥ 2\\n\\n    C(T)≥C(n):=nc(1)+(n-2)c(Δ(n...</td>\n",
       "      <td>(&lt;ref&gt;</td>\n",
       "      <td>\\nFor n ≥ 2\\n\\n    C(T)≥C(n):=nc(1)+(n-2)c(Δ(n...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1573</th>\n",
       "      <td>(;);\\ref{Fig.1;(i);(ii);(;);(iv);(v)</td>\n",
       "      <td>\\n\\label{CLTORDP}There exist five distinct tor...</td>\n",
       "      <td>/home/shufan/que_tex/One_Sing.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nThere exist five distinct toric del Pezzo su...</td>\n",
       "      <td>(;);&lt;ref&gt;</td>\n",
       "      <td>\\nThere exist five distinct toric del Pezzo su...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1574</th>\n",
       "      <td>(;);:\\smallskip;(i);(ii) ;conv;conv;conv;Figur...</td>\n",
       "      <td>\\n\\label{MAIN1}Let $X_{Q}$ be a toric log del ...</td>\n",
       "      <td>/home/shufan/que_tex/One_Sing.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet X_Q be a toric log del Pezzo surface (as...</td>\n",
       "      <td>(;);:;(i);(ii) ;conv;conv;conv;Figure &lt;ref&gt;</td>\n",
       "      <td>\\nLet X_Q be a toric log del Pezzo surface B_M...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1644</th>\n",
       "      <td>(\\ref{one</td>\n",
       "      <td>\\label{sun-complexity}\\nDetermining whether th...</td>\n",
       "      <td>/home/shufan/que_tex/1801.09170.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nDetermining whether the multiplicity (&lt;ref&gt; ...</td>\n",
       "      <td>(&lt;ref&gt;</td>\n",
       "      <td>\\nDetermining whether the multiplicity B_MATH_...</td>\n",
       "      <td>O O O O B_MATH_TERM O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1647</th>\n",
       "      <td>(\\ref{two;(\\ref{three</td>\n",
       "      <td>\\n Determining whether multiplicities \\emph{(\\...</td>\n",
       "      <td>/home/shufan/que_tex/1801.09170.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n Determining whether multiplicities (&lt;ref&gt; )...</td>\n",
       "      <td>(&lt;ref&gt;</td>\n",
       "      <td>\\n Determining whether multiplicities B_MATH_T...</td>\n",
       "      <td>O O O B_MATH_TERM O O B_MATH_TERM O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2092</th>\n",
       "      <td>See \\autoref{prelims1</td>\n",
       "      <td>\\label{mainthm_morally}\\label{undom_td}\\nEvery...</td>\n",
       "      <td>/home/shufan/que_tex/undom_td150218.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nEvery graph has a tree-decomposition (T,) of...</td>\n",
       "      <td>See &lt;ref&gt;</td>\n",
       "      <td>\\nEvery graph has a tree-decomposition (T,) of...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O B_...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2998</th>\n",
       "      <td>(\\ref{eq:faceboundaries</td>\n",
       "      <td>\\nLet $\\pi$ be a rotation system of a graph $...</td>\n",
       "      <td>/home/shufan/que_tex/hex-braces_arxiv.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet π be a rotation system of a graph G. Th...</td>\n",
       "      <td>(&lt;ref&gt;</td>\n",
       "      <td>\\nLet π be a rotation system of a graph G. Th...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3142</th>\n",
       "      <td>(\\ref{eq:psi-def;(\\ref{eq:psi-def</td>\n",
       "      <td>\\nIf $0&lt;b&lt;1$ and $a&gt;0$ then the function $\\mu\\...</td>\n",
       "      <td>/home/shufan/que_tex/1509.05120.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nIf 0&lt;b&lt;1 and a&gt;0 then the function μ→x^-a-μ(...</td>\n",
       "      <td>(&lt;ref&gt;</td>\n",
       "      <td>\\nIf 0&lt;b&lt;1 and a&gt;0 then the function μ→x^-a-μ(...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3237</th>\n",
       "      <td>\\eqref{HWbis</td>\n",
       "      <td>\\label{HWweight} For $g=q/r$ and $N \\equiv 1 ...</td>\n",
       "      <td>/home/shufan/que_tex/fahssi.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>For g=q/r and N ≡ 1 r , the number of micro-...</td>\n",
       "      <td>(&lt;ref&gt;)</td>\n",
       "      <td>For g=q/r and N ≡ 1 r , the number of micro-...</td>\n",
       "      <td>O O O O O O O O O O O O B_MATH_TERM O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3572</th>\n",
       "      <td>(\\ref{comp3;(\\ref{comp4</td>\n",
       "      <td>\\label{complexity}\\nThe problems given in the ...</td>\n",
       "      <td>/home/shufan/que_tex/1907.10137.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nThe problems given in the rectangles (&lt;ref&gt; ...</td>\n",
       "      <td>(&lt;ref&gt;</td>\n",
       "      <td>\\nThe problems given in the rectangles B_MATH_...</td>\n",
       "      <td>O O O O O O B_MATH_TERM O O B_MATH_TERM O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6648</th>\n",
       "      <td>Construction~\\ref{xmapstoy</td>\n",
       "      <td>\\label{x_mapsto_y}\\nLet $\\alpha,\\beta$ be two ...</td>\n",
       "      <td>/home/shufan/que_tex/1402.7158.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet α,β be two points of a MIF(k) ℱ such tha...</td>\n",
       "      <td>Construction &lt;ref&gt;</td>\n",
       "      <td>\\nLet α,β be two points of a MIF(k) ℱ such tha...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7189</th>\n",
       "      <td>(\\ref{eq_degree_index_condition23</td>\n",
       "      <td>\\label{theorem_C_sufficient}\\nAssume the follo...</td>\n",
       "      <td>/home/shufan/que_tex/MATCH21914.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nAssume the following inequalities hold:\\n\\n ...</td>\n",
       "      <td>(&lt;ref&gt;</td>\n",
       "      <td>\\nAssume the following inequalities hold:\\n\\n ...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7670</th>\n",
       "      <td>No.;No.;(i);(x);(ii);(xi);(iii);(xii);(iv);(xi...</td>\n",
       "      <td>\\n\\label{THM3}Up to isomorphism, there are exa...</td>\n",
       "      <td>/home/shufan/que_tex/Index_3.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nUp to isomorphism, there are exactly 18 tori...</td>\n",
       "      <td>No.;No.;(i);(x);(ii);(xi);(iii);(xii);(iv);(xi...</td>\n",
       "      <td>\\nUp to isomorphism, there are exactly 18 tori...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O B_MA...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8017</th>\n",
       "      <td>fig. \\arabic{fig;theorem \\ref{t1;statement \\re...</td>\n",
       "      <td>\\n\\label{t1}\\n\\nLet $D\\geq 3$ and $G$ be a gra...</td>\n",
       "      <td>/home/shufan/que_tex/On_Brooks.tex</td>\n",
       "      <td>theorem + \\textit{}</td>\n",
       "      <td>\\n\\n\\nLet D≥ 3 and G be a graph without clique...</td>\n",
       "      <td>fig. fig;theorem &lt;ref&gt;</td>\n",
       "      <td>\\n\\n\\nLet D≥ 3 and G be a graph without clique...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8930</th>\n",
       "      <td>\\eqref{HWbis</td>\n",
       "      <td>\\label{HWweight} For $g=q/r$ and $N \\equiv 1 ...</td>\n",
       "      <td>/home/shufan/que_tex/comb-norm.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>For g=q/r and N ≡ 1 r , the number of micros...</td>\n",
       "      <td>(&lt;ref&gt;)</td>\n",
       "      <td>For g=q/r and N ≡ 1 r , the number of micros...</td>\n",
       "      <td>O O O O O O O O O O O O B_MATH_TERM O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10077</th>\n",
       "      <td>(\\ref{eq:An2</td>\n",
       "      <td>\\nUsing the given initial conditions for $A$ a...</td>\n",
       "      <td>/home/shufan/que_tex/undecidable_no_appendix.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nUsing the given initial conditions for A and...</td>\n",
       "      <td>(&lt;ref&gt;</td>\n",
       "      <td>\\nUsing the given initial conditions for A and...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10177</th>\n",
       "      <td>\\ref{prop1</td>\n",
       "      <td>\\n\\label{prop2} With the same hypotheses as in...</td>\n",
       "      <td>/home/shufan/que_tex/1603.00242.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n With the same hypotheses as in Theorem &lt;ref...</td>\n",
       "      <td>&lt;ref&gt;</td>\n",
       "      <td>\\n With the same hypotheses as in Theorem B_MA...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10178</th>\n",
       "      <td>\\ref{prop1</td>\n",
       "      <td>\\n\\label{mo}With the same hypotheses as in The...</td>\n",
       "      <td>/home/shufan/que_tex/1603.00242.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nWith the same hypotheses as in Theorem &lt;ref&gt;...</td>\n",
       "      <td>&lt;ref&gt;</td>\n",
       "      <td>\\nWith the same hypotheses as in Theorem B_MAT...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10673</th>\n",
       "      <td>Condition~\\ref{cond-dil</td>\n",
       "      <td>\\label{thm-fpp-main}\\nConsider a sequence of r...</td>\n",
       "      <td>/home/shufan/que_tex/wdiam.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nConsider a sequence of random weighted graph...</td>\n",
       "      <td>Condition &lt;ref&gt;</td>\n",
       "      <td>\\nConsider a sequence of random weighted graph...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O B_MATH...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11568</th>\n",
       "      <td>Construction~\\ref{Construction</td>\n",
       "      <td>\\label{thm1}\\nLet $\\Gamma$ be a connected $(G,...</td>\n",
       "      <td>/home/shufan/que_tex/1703.00666.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet Γ be a connected (G,2)-arc-transitive di...</td>\n",
       "      <td>Construction &lt;ref&gt;</td>\n",
       "      <td>\\nLet Γ be a connected (G,2)-arc-transitive di...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11680</th>\n",
       "      <td>Proof  of Theorem \\ref{thm-shell;strong embedd...</td>\n",
       "      <td>\\label{leftweak} A reduction tree $R_G$ is sa...</td>\n",
       "      <td>/home/shufan/que_tex/shellable-aug30.tex</td>\n",
       "      <td>definition + \\textit{}</td>\n",
       "      <td>A reduction tree R_G is said to have the lef...</td>\n",
       "      <td>Proof  of Theorem &lt;ref&gt;</td>\n",
       "      <td>A reduction tree R_G is said to have the lef...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11710</th>\n",
       "      <td>(\\ref{2kvfig</td>\n",
       "      <td>\\label{wytsemi}\\nThe abstract Wythoff's const...</td>\n",
       "      <td>/home/shufan/que_tex/revised_Monson-Schulte.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nThe abstract Wythoff's construction describ...</td>\n",
       "      <td>(&lt;ref&gt;</td>\n",
       "      <td>\\nThe abstract Wythoff's construction describ...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12532</th>\n",
       "      <td>Conjecture~\\ref{diregular</td>\n",
       "      <td>\\label{2diregular}\\nLet $D$ be a digraph. If $...</td>\n",
       "      <td>/home/shufan/que_tex/dst-smf.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet D be a digraph. If Δ^-≤ 2 and Δ^+≤ 2, \\n...</td>\n",
       "      <td>Conjecture &lt;ref&gt;</td>\n",
       "      <td>\\nLet D be a digraph. If Δ^-≤ 2 and Δ^+≤ 2, \\n...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O B_MATH_TERM O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12650</th>\n",
       "      <td>(Theorem~\\ref{theorem_lifting</td>\n",
       "      <td>\\n\\emph{(Theorem~\\ref{theorem_lifting} )}\\nIf ...</td>\n",
       "      <td>/home/shufan/que_tex/lifting_arxiv.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n(Theorem &lt;ref&gt; )\\nIf 𝐀 varies smoothly in M^...</td>\n",
       "      <td>(Theorem &lt;ref&gt;</td>\n",
       "      <td>\\nB_MATH_TERM )\\nIf 𝐀 varies smoothly in M^d a...</td>\n",
       "      <td>B_MATH_TERM O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12651</th>\n",
       "      <td>(Theorem~\\ref{theorem_dual_characteristic_poly...</td>\n",
       "      <td>\\n\\emph{(Theorem~\\ref{theorem_dual_characteris...</td>\n",
       "      <td>/home/shufan/que_tex/lifting_arxiv.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n(Theorem &lt;ref&gt; )\\nIf 𝐁 is a dual of 𝐀 in ℝ^n...</td>\n",
       "      <td>(Theorem &lt;ref&gt;</td>\n",
       "      <td>\\nB_MATH_TERM )\\nIf 𝐁 is a dual of 𝐀 in ℝ^n,\\n...</td>\n",
       "      <td>B_MATH_TERM O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13161</th>\n",
       "      <td>block tree;Figure \\ref{fig:c2block</td>\n",
       "      <td>\\n\\label{defn::c2}\\nGiven a tree $T$, we defin...</td>\n",
       "      <td>/home/shufan/que_tex/Abs52.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\n\\nGiven a tree T, we define the (C,2)-block ...</td>\n",
       "      <td>block tree;Figure &lt;ref&gt;</td>\n",
       "      <td>\\n\\nGiven a tree T, we define the (C,2)-block ...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13162</th>\n",
       "      <td>Figure \\ref{fig::tracenonpath2</td>\n",
       "      <td>\\nGiven a $(C,i)$-block tree $H$ of $G$, $i \\g...</td>\n",
       "      <td>/home/shufan/que_tex/Abs52.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nGiven a (C,i)-block tree H of G, i ≥ 2, we d...</td>\n",
       "      <td>Figure &lt;ref&gt;</td>\n",
       "      <td>\\nGiven a (C,i)-block tree H of G, i ≥ 2, we d...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14275</th>\n",
       "      <td>(\\ref{p=p</td>\n",
       "      <td>\\n\\label{Tloostri}\\label{Tcab}Suppose that a g...</td>\n",
       "      <td>/home/shufan/que_tex/dforms.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nSuppose that a graph G=( V,E) has\\na vertex ...</td>\n",
       "      <td>(&lt;ref&gt;</td>\n",
       "      <td>\\nSuppose that a graph G=( V,E) has\\na vertex ...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14834</th>\n",
       "      <td>(;), ;Ehr;for all;(\\ref{hiEhrh;area</td>\n",
       "      <td>\\n\\label{SIGMAPMINDES}Let $P$ be an $M$-polygo...</td>\n",
       "      <td>/home/shufan/que_tex/Twelveptthm.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\nLet P be an M-polygon. If f:X(N,Σ\\n_P)⟶ X(N,...</td>\n",
       "      <td>(;), ;Ehr;for all;(&lt;ref&gt;</td>\n",
       "      <td>\\nLet P be an M-polygon. If f:X(N,Σ\\n_P)⟶ X(N,...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14839</th>\n",
       "      <td>(;);Ker;gcd;\\ref{NORMIERUNG</td>\n",
       "      <td>\\label{GLOBALTHM}\\n\\tThere is an equivariant \\...</td>\n",
       "      <td>/home/shufan/que_tex/Twelveptthm.tex</td>\n",
       "      <td>theorem + \\emph{}</td>\n",
       "      <td>\\n\\tThere is an equivariant \\t(w.r.t. the acti...</td>\n",
       "      <td>(;);Ker;gcd;&lt;ref&gt;</td>\n",
       "      <td>\\n\\tThere is an equivariant \\tB_MATH_TERMw.r.t...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                    term  \\\n",
       "316    Statement of Theorem \\ref{thm:singleton_b_is_a...   \n",
       "894    (\\ref{eq3.2_Ah_Bh;\\ref{def3.2_Asigma;circulant...   \n",
       "908                                  (\\ref{LB_M1_general   \n",
       "1573                (;);\\ref{Fig.1;(i);(ii);(;);(iv);(v)   \n",
       "1574   (;);:\\smallskip;(i);(ii) ;conv;conv;conv;Figur...   \n",
       "1644                                           (\\ref{one   \n",
       "1647                               (\\ref{two;(\\ref{three   \n",
       "2092                               See \\autoref{prelims1   \n",
       "2998                             (\\ref{eq:faceboundaries   \n",
       "3142                   (\\ref{eq:psi-def;(\\ref{eq:psi-def   \n",
       "3237                                        \\eqref{HWbis   \n",
       "3572                             (\\ref{comp3;(\\ref{comp4   \n",
       "6648                          Construction~\\ref{xmapstoy   \n",
       "7189                   (\\ref{eq_degree_index_condition23   \n",
       "7670   No.;No.;(i);(x);(ii);(xi);(iii);(xii);(iv);(xi...   \n",
       "8017   fig. \\arabic{fig;theorem \\ref{t1;statement \\re...   \n",
       "8930                                        \\eqref{HWbis   \n",
       "10077                                       (\\ref{eq:An2   \n",
       "10177                                         \\ref{prop1   \n",
       "10178                                         \\ref{prop1   \n",
       "10673                            Condition~\\ref{cond-dil   \n",
       "11568                     Construction~\\ref{Construction   \n",
       "11680  Proof  of Theorem \\ref{thm-shell;strong embedd...   \n",
       "11710                                       (\\ref{2kvfig   \n",
       "12532                          Conjecture~\\ref{diregular   \n",
       "12650                      (Theorem~\\ref{theorem_lifting   \n",
       "12651  (Theorem~\\ref{theorem_dual_characteristic_poly...   \n",
       "13161                 block tree;Figure \\ref{fig:c2block   \n",
       "13162                     Figure \\ref{fig::tracenonpath2   \n",
       "14275                                          (\\ref{p=p   \n",
       "14834                (;), ;Ehr;for all;(\\ref{hiEhrh;area   \n",
       "14839                        (;);Ker;gcd;\\ref{NORMIERUNG   \n",
       "\n",
       "                                                     def  \\\n",
       "316    \\n%\\label{thm:singleton_b_is_a_prime}\\n\\emph{S...   \n",
       "894    \\n\\label{th3.2_Asigma-s}Let $(a_{1},a_{2},\\ldo...   \n",
       "908    \\label{LB_M1_general_theorem}\\nFor $n \\ge 2$\\n...   \n",
       "1573   \\n\\label{CLTORDP}There exist five distinct tor...   \n",
       "1574   \\n\\label{MAIN1}Let $X_{Q}$ be a toric log del ...   \n",
       "1644   \\label{sun-complexity}\\nDetermining whether th...   \n",
       "1647   \\n Determining whether multiplicities \\emph{(\\...   \n",
       "2092   \\label{mainthm_morally}\\label{undom_td}\\nEvery...   \n",
       "2998    \\nLet $\\pi$ be a rotation system of a graph $...   \n",
       "3142   \\nIf $0<b<1$ and $a>0$ then the function $\\mu\\...   \n",
       "3237    \\label{HWweight} For $g=q/r$ and $N \\equiv 1 ...   \n",
       "3572   \\label{complexity}\\nThe problems given in the ...   \n",
       "6648   \\label{x_mapsto_y}\\nLet $\\alpha,\\beta$ be two ...   \n",
       "7189   \\label{theorem_C_sufficient}\\nAssume the follo...   \n",
       "7670   \\n\\label{THM3}Up to isomorphism, there are exa...   \n",
       "8017   \\n\\label{t1}\\n\\nLet $D\\geq 3$ and $G$ be a gra...   \n",
       "8930    \\label{HWweight} For $g=q/r$ and $N \\equiv 1 ...   \n",
       "10077  \\nUsing the given initial conditions for $A$ a...   \n",
       "10177  \\n\\label{prop2} With the same hypotheses as in...   \n",
       "10178  \\n\\label{mo}With the same hypotheses as in The...   \n",
       "10673  \\label{thm-fpp-main}\\nConsider a sequence of r...   \n",
       "11568  \\label{thm1}\\nLet $\\Gamma$ be a connected $(G,...   \n",
       "11680   \\label{leftweak} A reduction tree $R_G$ is sa...   \n",
       "11710   \\label{wytsemi}\\nThe abstract Wythoff's const...   \n",
       "12532  \\label{2diregular}\\nLet $D$ be a digraph. If $...   \n",
       "12650  \\n\\emph{(Theorem~\\ref{theorem_lifting} )}\\nIf ...   \n",
       "12651  \\n\\emph{(Theorem~\\ref{theorem_dual_characteris...   \n",
       "13161  \\n\\label{defn::c2}\\nGiven a tree $T$, we defin...   \n",
       "13162  \\nGiven a $(C,i)$-block tree $H$ of $G$, $i \\g...   \n",
       "14275  \\n\\label{Tloostri}\\label{Tcab}Suppose that a g...   \n",
       "14834  \\n\\label{SIGMAPMINDES}Let $P$ be an $M$-polygo...   \n",
       "14839  \\label{GLOBALTHM}\\n\\tThere is an equivariant \\...   \n",
       "\n",
       "                                              file_name  \\\n",
       "316                 /home/shufan/que_tex/1803.03954.tex   \n",
       "894                  /home/shufan/que_tex/1203.0709.tex   \n",
       "908                     /home/shufan/que_tex/Goubko.tex   \n",
       "1573                  /home/shufan/que_tex/One_Sing.tex   \n",
       "1574                  /home/shufan/que_tex/One_Sing.tex   \n",
       "1644                /home/shufan/que_tex/1801.09170.tex   \n",
       "1647                /home/shufan/que_tex/1801.09170.tex   \n",
       "2092            /home/shufan/que_tex/undom_td150218.tex   \n",
       "2998          /home/shufan/que_tex/hex-braces_arxiv.tex   \n",
       "3142                /home/shufan/que_tex/1509.05120.tex   \n",
       "3237                    /home/shufan/que_tex/fahssi.tex   \n",
       "3572                /home/shufan/que_tex/1907.10137.tex   \n",
       "6648                 /home/shufan/que_tex/1402.7158.tex   \n",
       "7189                /home/shufan/que_tex/MATCH21914.tex   \n",
       "7670                   /home/shufan/que_tex/Index_3.tex   \n",
       "8017                 /home/shufan/que_tex/On_Brooks.tex   \n",
       "8930                 /home/shufan/que_tex/comb-norm.tex   \n",
       "10077  /home/shufan/que_tex/undecidable_no_appendix.tex   \n",
       "10177               /home/shufan/que_tex/1603.00242.tex   \n",
       "10178               /home/shufan/que_tex/1603.00242.tex   \n",
       "10673                    /home/shufan/que_tex/wdiam.tex   \n",
       "11568               /home/shufan/que_tex/1703.00666.tex   \n",
       "11680          /home/shufan/que_tex/shellable-aug30.tex   \n",
       "11710   /home/shufan/que_tex/revised_Monson-Schulte.tex   \n",
       "12532                  /home/shufan/que_tex/dst-smf.tex   \n",
       "12650            /home/shufan/que_tex/lifting_arxiv.tex   \n",
       "12651            /home/shufan/que_tex/lifting_arxiv.tex   \n",
       "13161                    /home/shufan/que_tex/Abs52.tex   \n",
       "13162                    /home/shufan/que_tex/Abs52.tex   \n",
       "14275                   /home/shufan/que_tex/dforms.tex   \n",
       "14834              /home/shufan/que_tex/Twelveptthm.tex   \n",
       "14839              /home/shufan/que_tex/Twelveptthm.tex   \n",
       "\n",
       "              extraction_rule  \\\n",
       "316         theorem + \\emph{}   \n",
       "894         theorem + \\emph{}   \n",
       "908         theorem + \\emph{}   \n",
       "1573        theorem + \\emph{}   \n",
       "1574        theorem + \\emph{}   \n",
       "1644        theorem + \\emph{}   \n",
       "1647        theorem + \\emph{}   \n",
       "2092        theorem + \\emph{}   \n",
       "2998        theorem + \\emph{}   \n",
       "3142        theorem + \\emph{}   \n",
       "3237        theorem + \\emph{}   \n",
       "3572        theorem + \\emph{}   \n",
       "6648        theorem + \\emph{}   \n",
       "7189        theorem + \\emph{}   \n",
       "7670        theorem + \\emph{}   \n",
       "8017      theorem + \\textit{}   \n",
       "8930        theorem + \\emph{}   \n",
       "10077       theorem + \\emph{}   \n",
       "10177       theorem + \\emph{}   \n",
       "10178       theorem + \\emph{}   \n",
       "10673       theorem + \\emph{}   \n",
       "11568       theorem + \\emph{}   \n",
       "11680  definition + \\textit{}   \n",
       "11710       theorem + \\emph{}   \n",
       "12532       theorem + \\emph{}   \n",
       "12650       theorem + \\emph{}   \n",
       "12651       theorem + \\emph{}   \n",
       "13161    definition + \\emph{}   \n",
       "13162    definition + \\emph{}   \n",
       "14275       theorem + \\emph{}   \n",
       "14834       theorem + \\emph{}   \n",
       "14839       theorem + \\emph{}   \n",
       "\n",
       "                                          plain_text_def  \\\n",
       "316    \\n\\nStatement of Theorem <ref>: Let n be a pos...   \n",
       "894    \\nLet (a_1,a_2,… ,a_k) be a\\n(v,k) modular Gol...   \n",
       "908    \\nFor n ≥ 2\\n\\n    C(T)≥C(n):=nc(1)+(n-2)c(Δ(n...   \n",
       "1573   \\nThere exist five distinct toric del Pezzo su...   \n",
       "1574   \\nLet X_Q be a toric log del Pezzo surface (as...   \n",
       "1644   \\nDetermining whether the multiplicity (<ref> ...   \n",
       "1647   \\n Determining whether multiplicities (<ref> )...   \n",
       "2092   \\nEvery graph has a tree-decomposition (T,) of...   \n",
       "2998    \\nLet π be a rotation system of a graph G. Th...   \n",
       "3142   \\nIf 0<b<1 and a>0 then the function μ→x^-a-μ(...   \n",
       "3237     For g=q/r and N ≡ 1 r , the number of micro-...   \n",
       "3572   \\nThe problems given in the rectangles (<ref> ...   \n",
       "6648   \\nLet α,β be two points of a MIF(k) ℱ such tha...   \n",
       "7189   \\nAssume the following inequalities hold:\\n\\n ...   \n",
       "7670   \\nUp to isomorphism, there are exactly 18 tori...   \n",
       "8017   \\n\\n\\nLet D≥ 3 and G be a graph without clique...   \n",
       "8930     For g=q/r and N ≡ 1 r , the number of micros...   \n",
       "10077  \\nUsing the given initial conditions for A and...   \n",
       "10177  \\n With the same hypotheses as in Theorem <ref...   \n",
       "10178  \\nWith the same hypotheses as in Theorem <ref>...   \n",
       "10673  \\nConsider a sequence of random weighted graph...   \n",
       "11568  \\nLet Γ be a connected (G,2)-arc-transitive di...   \n",
       "11680    A reduction tree R_G is said to have the lef...   \n",
       "11710   \\nThe abstract Wythoff's construction describ...   \n",
       "12532  \\nLet D be a digraph. If Δ^-≤ 2 and Δ^+≤ 2, \\n...   \n",
       "12650  \\n(Theorem <ref> )\\nIf 𝐀 varies smoothly in M^...   \n",
       "12651  \\n(Theorem <ref> )\\nIf 𝐁 is a dual of 𝐀 in ℝ^n...   \n",
       "13161  \\n\\nGiven a tree T, we define the (C,2)-block ...   \n",
       "13162  \\nGiven a (C,i)-block tree H of G, i ≥ 2, we d...   \n",
       "14275  \\nSuppose that a graph G=( V,E) has\\na vertex ...   \n",
       "14834  \\nLet P be an M-polygon. If f:X(N,Σ\\n_P)⟶ X(N,...   \n",
       "14839  \\n\\tThere is an equivariant \\t(w.r.t. the acti...   \n",
       "\n",
       "                                         plain_text_term  \\\n",
       "316                           Statement of Theorem <ref>   \n",
       "894                                               (<ref>   \n",
       "908                                               (<ref>   \n",
       "1573                                           (;);<ref>   \n",
       "1574         (;);:;(i);(ii) ;conv;conv;conv;Figure <ref>   \n",
       "1644                                              (<ref>   \n",
       "1647                                              (<ref>   \n",
       "2092                                           See <ref>   \n",
       "2998                                              (<ref>   \n",
       "3142                                              (<ref>   \n",
       "3237                                             (<ref>)   \n",
       "3572                                              (<ref>   \n",
       "6648                                  Construction <ref>   \n",
       "7189                                              (<ref>   \n",
       "7670   No.;No.;(i);(x);(ii);(xi);(iii);(xii);(iv);(xi...   \n",
       "8017                              fig. fig;theorem <ref>   \n",
       "8930                                             (<ref>)   \n",
       "10077                                             (<ref>   \n",
       "10177                                              <ref>   \n",
       "10178                                              <ref>   \n",
       "10673                                    Condition <ref>   \n",
       "11568                                 Construction <ref>   \n",
       "11680                            Proof  of Theorem <ref>   \n",
       "11710                                             (<ref>   \n",
       "12532                                   Conjecture <ref>   \n",
       "12650                                     (Theorem <ref>   \n",
       "12651                                     (Theorem <ref>   \n",
       "13161                            block tree;Figure <ref>   \n",
       "13162                                       Figure <ref>   \n",
       "14275                                             (<ref>   \n",
       "14834                           (;), ;Ehr;for all;(<ref>   \n",
       "14839                                  (;);Ker;gcd;<ref>   \n",
       "\n",
       "                                   masked_plain_text_def  \\\n",
       "316    \\n\\nB_MATH_TERM I_MATH_TERM I_MATH_TERM I_MATH...   \n",
       "894    \\nLet (a_1,a_2,… ,a_k) be a\\n(v,k) modular Gol...   \n",
       "908    \\nFor n ≥ 2\\n\\n    C(T)≥C(n):=nc(1)+(n-2)c(Δ(n...   \n",
       "1573   \\nThere exist five distinct toric del Pezzo su...   \n",
       "1574   \\nLet X_Q be a toric log del Pezzo surface B_M...   \n",
       "1644   \\nDetermining whether the multiplicity B_MATH_...   \n",
       "1647   \\n Determining whether multiplicities B_MATH_T...   \n",
       "2092   \\nEvery graph has a tree-decomposition (T,) of...   \n",
       "2998    \\nLet π be a rotation system of a graph G. Th...   \n",
       "3142   \\nIf 0<b<1 and a>0 then the function μ→x^-a-μ(...   \n",
       "3237     For g=q/r and N ≡ 1 r , the number of micro-...   \n",
       "3572   \\nThe problems given in the rectangles B_MATH_...   \n",
       "6648   \\nLet α,β be two points of a MIF(k) ℱ such tha...   \n",
       "7189   \\nAssume the following inequalities hold:\\n\\n ...   \n",
       "7670   \\nUp to isomorphism, there are exactly 18 tori...   \n",
       "8017   \\n\\n\\nLet D≥ 3 and G be a graph without clique...   \n",
       "8930     For g=q/r and N ≡ 1 r , the number of micros...   \n",
       "10077  \\nUsing the given initial conditions for A and...   \n",
       "10177  \\n With the same hypotheses as in Theorem B_MA...   \n",
       "10178  \\nWith the same hypotheses as in Theorem B_MAT...   \n",
       "10673  \\nConsider a sequence of random weighted graph...   \n",
       "11568  \\nLet Γ be a connected (G,2)-arc-transitive di...   \n",
       "11680    A reduction tree R_G is said to have the lef...   \n",
       "11710   \\nThe abstract Wythoff's construction describ...   \n",
       "12532  \\nLet D be a digraph. If Δ^-≤ 2 and Δ^+≤ 2, \\n...   \n",
       "12650  \\nB_MATH_TERM )\\nIf 𝐀 varies smoothly in M^d a...   \n",
       "12651  \\nB_MATH_TERM )\\nIf 𝐁 is a dual of 𝐀 in ℝ^n,\\n...   \n",
       "13161  \\n\\nGiven a tree T, we define the (C,2)-block ...   \n",
       "13162  \\nGiven a (C,i)-block tree H of G, i ≥ 2, we d...   \n",
       "14275  \\nSuppose that a graph G=( V,E) has\\na vertex ...   \n",
       "14834  \\nLet P be an M-polygon. If f:X(N,Σ\\n_P)⟶ X(N,...   \n",
       "14839  \\n\\tThere is an equivariant \\tB_MATH_TERMw.r.t...   \n",
       "\n",
       "                                             labeled_def  \n",
       "316    B_MATH_TERM I_MATH_TERM I_MATH_TERM O O O O O ...  \n",
       "894    O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "908    O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "1573   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "1574   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "1644   O O O O B_MATH_TERM O O O O O O O O O O O O O ...  \n",
       "1647   O O O B_MATH_TERM O O B_MATH_TERM O O O O O O ...  \n",
       "2092   O O O O O O O O O O O O O O O O O O O O O O B_...  \n",
       "2998   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "3142   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "3237   O O O O O O O O O O O O B_MATH_TERM O O O O O ...  \n",
       "3572       O O O O O O B_MATH_TERM O O B_MATH_TERM O O O  \n",
       "6648   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "7189   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "7670   O O O O O O O O O O O O O O O O O O O O O B_MA...  \n",
       "8017   O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "8930   O O O O O O O O O O O O B_MATH_TERM O O O O O ...  \n",
       "10077  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "10177  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "10178  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "10673  O O O O O O O O O O O O O O O O O O O O B_MATH...  \n",
       "11568  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "11680  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "11710  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "12532  O O O O O O O O O O O O O O O O B_MATH_TERM O ...  \n",
       "12650  B_MATH_TERM O O O O O O O O O O O O O O O O O ...  \n",
       "12651  B_MATH_TERM O O O O O O O O O O O O O O O O O ...  \n",
       "13161  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "13162  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "14275  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "14834  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "14839  O O O O O O O O O O O O O O O O O O O O O O O ...  "
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_clean[df_clean['plain_text_term'].str.contains('<ref')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "735bf09a-c70b-46b4-b5f9-d11f55999427",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean = df_clean[~df_clean['plain_text_term'].str.contains('<ref')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "50fdc25f-831f-432e-9ec2-784a7e524f29",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean.to_csv('cleaned_plain-text_term+combined_no_ref_no_cit_def_labeled.csv',index=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "03adb55c-3194-413a-a513-496ddd1be5d8",
   "metadata": {},
   "source": [
    "## TODO: why some label strings have no B-MATH_TERM? And why some of these contains I-MATH_TERM???"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "bdffe17b-bd12-4719-98ea-e194d1e92c29",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13692"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#df = pd.read_csv(\"cleaned_plain-text_labeled_term+combined_no_ref_no_cit_def_same_len_only.csv\", delimiter=',')\n",
    "df = pd.read_csv(\"cleaned_plain-text_labeled_term+combined_no_ref_no_cit_def_same_len_only_must_conatin_B.csv\", delimiter=',')\n",
    "len(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "c595ccc1-0b61-46b6-8e24-b237b8909854",
   "metadata": {},
   "outputs": [],
   "source": [
    "O_then_I = df[df['labeled_def'].str.contains('O I_MATH_TERM')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "3e66a0ac-0c51-4e49-8348-7229bb66130d",
   "metadata": {},
   "outputs": [],
   "source": [
    "must_b = df[df['labeled_def'].str.contains('B_MATH_TERM')]\n",
    "must_b = must_b[~must_b['labeled_def'].str.contains('O I_MATH_TERM')]\n",
    "must_b.to_csv(\"cleaned_plain-text_labeled_term+combined_no_ref_no_cit_def_same_len_only_must_conatin_B.csv\", index=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "2605d256-130e-4b6a-be93-e19e494ea8ec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "term                     48\n",
       "def                      48\n",
       "file_name                48\n",
       "extraction_rule          48\n",
       "plain_text_def           48\n",
       "plain_text_term          48\n",
       "masked_plain_text_def    48\n",
       "labeled_def              48\n",
       "dtype: int64"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "O_then_I.count()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1005f57e-2a3d-428c-8467-8f88803abe3f",
   "metadata": {},
   "outputs": [],
   "source": [
    "no_b = df[~df['labeled_def'].str.contains('B_MATH_TERM')]\n",
    "no_b "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "56d486d7-e4a0-4c93-a051-da7b39058ecb",
   "metadata": {},
   "outputs": [],
   "source": [
    "no_b.to_csv(\"cleaned_plain-text_labeled_term+combined_no_ref_no_cit_def_same_len_only_why_no_B.csv\", index=False)\n",
    "\n",
    "no_b_but_i = no_b[no_b['labeled_def'].str.contains('I_MATH_TERM')]\n",
    "no_b_but_i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "a0f88f01-5253-4b05-a725-42ace35ed291",
   "metadata": {},
   "outputs": [],
   "source": [
    "no_b_but_i.to_csv(\"cleaned_plain-text_labeled_term+combined_no_ref_no_cit_def_same_len_only_why_no_B_but_I.csv\",index= False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2fd3c31-f4e8-4649-9167-47df4ff6bf24",
   "metadata": {},
   "source": [
    "## TODO: XXX-B_MATH_TERM are lost \n",
    "def 19\tA \\emph{$Z$-oriented spanning forest} of $G$ is an oriented subgraph $F$ of $G$ such that...\n",
    "\n",
    "This line is extracted with the definition[] rule, as in the [] it is noted as \"Oriented spanning forest\", in the {},it is written \"\\emph{$Z$-oriented spanning forest}\"\n",
    "so the masked plained text is:\n",
    "\t\n",
    "A Z-B_MATH_TERM I_MATH_TERM I_MATH_TERM of G is an oriented subgraph F of G such that...\n",
    "\n",
    "However, as we have dealed with \\emph{} apart, this text shouble be doubled"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "19edf093-1399-41d3-94f9-ad8cc076f014",
   "metadata": {},
   "source": [
    "## TODO: Notions \\textit{E} and \\textit{F}\n",
    "Let $\\mathcal{C}$ be a conic inscribed in an octagon $A B C D E F\n",
    "G H$, let $\\textit{E}$ be a conic touching some four sides of the\n",
    "octagon, and $\\textit{F}$ be a conic touching the remaining four\n",
    "sides of octagons. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "99f67535-e4f0-43e1-900d-ba51c6cef859",
   "metadata": {},
   "source": [
    "## TODO:   of \\emph{Type} $\\cal M$\n",
    "\\label{definition3}(Auxiliary definition) Let $q+1$ be an odd integer. An edge-coloring $\\varsigma\\colon E(K_{q+2}) \\rightarrow [q+1]$ is of \\emph{Type} $\\cal M$, if for every $i\\in [q+1]$ the set of edges $\\varsigma^{-1}(i)$ is a perfect matching of $K_{q+2}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3626bb3-5ebc-4025-9211-86fb521f56fa",
   "metadata": {},
   "source": [
    "## TODO: These are not terms\n",
    "\tplain_text_term\n",
    "76\tatoms;supp(p)-{p_1}∈𝒮_P;supp\n",
    "\n",
    "\tmasked_plain_text_def\n",
    "76\t\n",
    "Let P be a finite atomic lattice. Then P is super-atomic if and only if for any p∈ P-B_MATH_TERM(P)⋃{0}, there exist two atoms p_1,  p_2 in P such that p= p_1∨ p_2 satisfying that B_MATH_TERM andB_MATH_TERM(p)-{p_2}∈𝒮_P.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b78c5f9e-4512-407a-9ea6-617bc1ede9d3",
   "metadata": {},
   "source": [
    "## TODO: The \"at\" is not a term, the terms should be \"simple local complement of S at i\"\n",
    "\\label{lc} Let $S$ be a symmetric $n\\times n$ matrix, and suppose $1\\leq i\\leq\n",
    "n$. Then the \\emph{simple local complement of }$S$ \\emph{at} $i$ is the\n",
    "symmetric $GF(2)$-matrix $S^{i}$ obtained from $S$ as follows: whenever $i\\neq\n",
    "j\\neq k\\neq i$ and $s_{ij}\\neq0\\neq s_{ik}$, toggle $s_{jk}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ebb45daf-ac29-4f81-80ed-2f9a44b30226",
   "metadata": {},
   "source": [
    "## TODO: \\textit{n} might be $n$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9be8f0a1-ed16-4bae-ba26-a02db9798b1c",
   "metadata": {},
   "source": [
    "## TODO: \\emph{f}ar-\\emph{a}part \\emph{n}ine\n",
    "A subset $\\mathcal{F}$ of nine points of a $\\mathcal{S}_{3}(2)$ is a\n",
    "\\emph{fan} (= \\emph{f}ar-\\emph{a}part \\emph{n}ine) if no two points of\n",
    "$\\mathcal{F}$ lie on the same generator. (So if $\\mathcal{F}$ is a fan for a\n",
    "$\\mathcal{S}_{3}(2)$ then the 3 generators through each of the 9 points of\n",
    "$\\mathcal{F}$ account for all $3\\times9=27$ generators of $\\mathcal{S}%\n",
    "_{3}(2).$)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "efdb9943-7e5b-4a38-a76c-f99a486b8585",
   "metadata": {},
   "outputs": [],
   "source": [
    "combi_pattern = r'(\\\\emph\\{.*?\\}(a-zA-Z|$))|(\\\\textit\\{.*?\\}(a-zA-Z|$))'\n",
    "\n",
    "df_clean[df_clean['def'].str.contains(combi_pattern)]#.to_csv('test_more_combi.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8ec6129f-96f2-4805-916a-ff0745285c8c",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean[df_clean['def'].str.contains(combi_pattern)].to_csv('test_more_combi.csv',index=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "19170f65-5abd-41ae-838d-3cc0e872c173",
   "metadata": {},
   "source": [
    "# Check plain text length & labeled_def length !!!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "dcb7374d-a00d-43fc-88e2-684705a6bf73",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    .dataframe tbody tr th {\n",
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       "    }\n",
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       "    .dataframe thead th {\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>term</th>\n",
       "      <th>def</th>\n",
       "      <th>file_name</th>\n",
       "      <th>extraction_rule</th>\n",
       "      <th>plain_text_def</th>\n",
       "      <th>plain_text_term</th>\n",
       "      <th>masked_plain_text_def</th>\n",
       "      <th>labeled_def</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>14914</th>\n",
       "      <td>preferred direction;special claw corresponding...</td>\n",
       "      <td>\\label{definition:SpecialClaw} Consider $\\lang...</td>\n",
       "      <td>/home/shufan/que_tex/CosetsVoltagesAndDerivedE...</td>\n",
       "      <td>definition + \\textit{}</td>\n",
       "      <td>Consider ⟨ G→ S, α→ A⟩, two adjacent vertices...</td>\n",
       "      <td>preferred direction;special claw corresponding...</td>\n",
       "      <td>Consider ⟨ G→ S, α→ A⟩, two adjacent vertices...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14915</th>\n",
       "      <td>Cyclicity classes</td>\n",
       "      <td>\\label{d:cyclasses}\\nAccording to Theorem~\\ref...</td>\n",
       "      <td>/home/shufan/que_tex/1307.3716.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>\\nAccording to Theorem &lt;ref&gt;, ^d has exactly d...</td>\n",
       "      <td>Cyclicity classes</td>\n",
       "      <td>\\nAccording to Theorem &lt;ref&gt;, ^d has exactly d...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14916</th>\n",
       "      <td>Wielandt number</td>\n",
       "      <td>By {\\em Wielandt number} we mean the following...</td>\n",
       "      <td>/home/shufan/que_tex/1307.3716.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>By Wielandt number we mean the following funct...</td>\n",
       "      <td>Wielandt number</td>\n",
       "      <td>By B_MATH_TERM I_MATH_TERM we mean the followi...</td>\n",
       "      <td>O B_MATH_TERM I_MATH_TERM O O O O O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14917</th>\n",
       "      <td>Girth</td>\n",
       "      <td>\\label{d:girth}\\nThe {\\em girth\\/} of $\\digr$,...</td>\n",
       "      <td>/home/shufan/que_tex/1307.3716.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>\\nThe girth of , denoted it by g(),\\nis the sm...</td>\n",
       "      <td>Girth</td>\n",
       "      <td>\\nThe B_MATH_TERM of , denoted it by g(),\\nis ...</td>\n",
       "      <td>O B_MATH_TERM O O O O O O O O O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14918</th>\n",
       "      <td>Critical graph</td>\n",
       "      <td>\\label{d:crit}\\nLet $A\\in\\Rpnn$. The cycles of...</td>\n",
       "      <td>/home/shufan/que_tex/1307.3716.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>\\nLet A∈. The cycles of (A) at which the maxim...</td>\n",
       "      <td>Critical graph</td>\n",
       "      <td>\\nLet A∈. The cycles of (A) at which the maxim...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                    term  \\\n",
       "14914  preferred direction;special claw corresponding...   \n",
       "14915                                  Cyclicity classes   \n",
       "14916                                    Wielandt number   \n",
       "14917                                              Girth   \n",
       "14918                                     Critical graph   \n",
       "\n",
       "                                                     def  \\\n",
       "14914  \\label{definition:SpecialClaw} Consider $\\lang...   \n",
       "14915  \\label{d:cyclasses}\\nAccording to Theorem~\\ref...   \n",
       "14916  By {\\em Wielandt number} we mean the following...   \n",
       "14917  \\label{d:girth}\\nThe {\\em girth\\/} of $\\digr$,...   \n",
       "14918  \\label{d:crit}\\nLet $A\\in\\Rpnn$. The cycles of...   \n",
       "\n",
       "                                               file_name  \\\n",
       "14914  /home/shufan/que_tex/CosetsVoltagesAndDerivedE...   \n",
       "14915                 /home/shufan/que_tex/1307.3716.tex   \n",
       "14916                 /home/shufan/que_tex/1307.3716.tex   \n",
       "14917                 /home/shufan/que_tex/1307.3716.tex   \n",
       "14918                 /home/shufan/que_tex/1307.3716.tex   \n",
       "\n",
       "              extraction_rule  \\\n",
       "14914  definition + \\textit{}   \n",
       "14915            definition[]   \n",
       "14916            definition[]   \n",
       "14917            definition[]   \n",
       "14918            definition[]   \n",
       "\n",
       "                                          plain_text_def  \\\n",
       "14914   Consider ⟨ G→ S, α→ A⟩, two adjacent vertices...   \n",
       "14915  \\nAccording to Theorem <ref>, ^d has exactly d...   \n",
       "14916  By Wielandt number we mean the following funct...   \n",
       "14917  \\nThe girth of , denoted it by g(),\\nis the sm...   \n",
       "14918  \\nLet A∈. The cycles of (A) at which the maxim...   \n",
       "\n",
       "                                         plain_text_term  \\\n",
       "14914  preferred direction;special claw corresponding...   \n",
       "14915                                  Cyclicity classes   \n",
       "14916                                    Wielandt number   \n",
       "14917                                              Girth   \n",
       "14918                                     Critical graph   \n",
       "\n",
       "                                   masked_plain_text_def  \\\n",
       "14914   Consider ⟨ G→ S, α→ A⟩, two adjacent vertices...   \n",
       "14915  \\nAccording to Theorem <ref>, ^d has exactly d...   \n",
       "14916  By B_MATH_TERM I_MATH_TERM we mean the followi...   \n",
       "14917  \\nThe B_MATH_TERM of , denoted it by g(),\\nis ...   \n",
       "14918  \\nLet A∈. The cycles of (A) at which the maxim...   \n",
       "\n",
       "                                             labeled_def  \n",
       "14914  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "14915  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "14916  O B_MATH_TERM I_MATH_TERM O O O O O O O O O O O O  \n",
       "14917      O B_MATH_TERM O O O O O O O O O O O O O O O O  \n",
       "14918  O O O O O O O O O O O O O O O O O O O O O O O ...  "
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_clean = pd.read_csv('cleaned_plain-text_term+combined_no_ref_no_cit_def_labeled.csv')\n",
    "df_clean.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "43e15f35-8ce9-49cb-891c-d5c0999ef070",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "term                     774\n",
       "def                      774\n",
       "file_name                774\n",
       "extraction_rule          774\n",
       "plain_text_def           774\n",
       "plain_text_term          774\n",
       "masked_plain_text_def    774\n",
       "labeled_def              774\n",
       "diff_tokens              774\n",
       "dtype: int64"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_clean['diff_tokens'] = df_clean.apply(lambda row: len(row['plain_text_def'].split()) != len(row['labeled_def'].split()), axis=1)\n",
    "df_clean[df_clean['diff_tokens']].count()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "d053def4-8555-42bb-804e-171a6463927c",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean[df_clean['diff_tokens']].to_csv(\"diff_tokens.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "7f9f3888-15a1-40d8-8399-543d2f1e4974",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(\"B_MATH_TERM\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "871c6f54-4ec0-47a9-bd3f-837a813a6852",
   "metadata": {},
   "outputs": [],
   "source": [
    "MATH_TERM_phrases = {\"I_MATH_TERM,\"}\n",
    "\n",
    "for sent in df_clean['masked_plain_text_def']:\n",
    "    tokens = sent.split()\n",
    "    for token in tokens:\n",
    "        if ('B_MATH_TERM' in token or 'I_MATH_TERM' in token) and len(token) > 11:\n",
    "            MATH_TERM_phrases.add(token)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "de19903c-1867-4e52-8d5a-35612b191d32",
   "metadata": {},
   "outputs": [],
   "source": [
    "#note this phrases to a txt file\n",
    "my_set_str = str(MATH_TERM_phrases)\n",
    "\n",
    "# Open a new file for writing\n",
    "with open('tokens_that_contains_B_I_MATH_TERM.txt', 'w') as f:\n",
    "    # Write the string to the file\n",
    "    f.write(my_set_str)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "b3771275-cb3d-44ed-8568-1983bfde6195",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "term                     0\n",
       "def                      0\n",
       "file_name                0\n",
       "extraction_rule          0\n",
       "plain_text_def           0\n",
       "plain_text_term          0\n",
       "masked_plain_text_def    0\n",
       "labeled_def              0\n",
       "diff_tokens              0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_clean['diff_tokens'] = df_clean.apply(lambda row: len(row['masked_plain_text_def'].split()) != len(row['labeled_def'].split()), axis=1)\n",
    "df_clean[df_clean['diff_tokens']].count()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "5711d6b5-b111-48af-a43b-effa321a6f21",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "term                     774\n",
       "def                      774\n",
       "file_name                774\n",
       "extraction_rule          774\n",
       "plain_text_def           774\n",
       "plain_text_term          774\n",
       "masked_plain_text_def    774\n",
       "labeled_def              774\n",
       "diff_tokens              774\n",
       "dtype: int64"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_clean['diff_tokens'] = df_clean.apply(lambda row: len(row['plain_text_def'].split()) != len(row['labeled_def'].split()), axis=1)\n",
    "df_clean[df_clean['diff_tokens']].count()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "1e23340f-97e7-422f-9c31-af885434b30e",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>term</th>\n",
       "      <th>def</th>\n",
       "      <th>file_name</th>\n",
       "      <th>extraction_rule</th>\n",
       "      <th>plain_text_def</th>\n",
       "      <th>plain_text_term</th>\n",
       "      <th>masked_plain_text_def</th>\n",
       "      <th>labeled_def</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>admissible $G$-cover</td>\n",
       "      <td>\\label{def_admissibleGcover}\\nLet $G$ be a fin...</td>\n",
       "      <td>/home/shufan/que_tex/abelian_tropical_covers.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\nLet G be a finite group and let X→ S be a fa...</td>\n",
       "      <td>admissible G-cover</td>\n",
       "      <td>\\nLet G be a finite group and let X→ S be a fa...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>light reduction pair;heavy reduction pair</td>\n",
       "      <td>\\n  Let $\\pi\\in\\fs_n$ and let $x,y$ be a pair ...</td>\n",
       "      <td>/home/shufan/que_tex/Post071005.tex</td>\n",
       "      <td>definition + \\emph{}</td>\n",
       "      <td>\\n  Let π∈_n and let x,y be a pair of rooks th...</td>\n",
       "      <td>light reduction pair;heavy reduction pair</td>\n",
       "      <td>\\n  Let π∈_n and let x,y be a pair of rooks th...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O B_...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Local modification rule</td>\n",
       "      <td>\\label{lacma}  A \\emph{local modification rule...</td>\n",
       "      <td>/home/shufan/que_tex/hereditary_submit.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>A local modification rule is a pair (A,T), w...</td>\n",
       "      <td>Local modification rule</td>\n",
       "      <td>A B_MATH_TERM I_MATH_TERM I_MATH_TERM is a p...</td>\n",
       "      <td>O B_MATH_TERM I_MATH_TERM I_MATH_TERM O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Vertex sets</td>\n",
       "      <td>\\label{vertset}  A \\emph{vertex set} is any se...</td>\n",
       "      <td>/home/shufan/que_tex/hereditary_submit.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>A vertex set is any set which is at most cou...</td>\n",
       "      <td>Vertex sets</td>\n",
       "      <td>A vertex set is any set which is at most cou...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O B_MATH_TERM O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Palettes</td>\n",
       "      <td>A \\emph{finite palette} is a sequence $K = (K_...</td>\n",
       "      <td>/home/shufan/que_tex/hereditary_submit.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>A finite palette is a sequence K = (K_j)_j=0^∞...</td>\n",
       "      <td>Palettes</td>\n",
       "      <td>A finite palette is a sequence K = (K_j)_j=0^∞...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14914</th>\n",
       "      <td>preferred direction;special claw corresponding...</td>\n",
       "      <td>\\label{definition:SpecialClaw} Consider $\\lang...</td>\n",
       "      <td>/home/shufan/que_tex/CosetsVoltagesAndDerivedE...</td>\n",
       "      <td>definition + \\textit{}</td>\n",
       "      <td>Consider ⟨ G→ S, α→ A⟩, two adjacent vertices...</td>\n",
       "      <td>preferred direction;special claw corresponding...</td>\n",
       "      <td>Consider ⟨ G→ S, α→ A⟩, two adjacent vertices...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14915</th>\n",
       "      <td>Cyclicity classes</td>\n",
       "      <td>\\label{d:cyclasses}\\nAccording to Theorem~\\ref...</td>\n",
       "      <td>/home/shufan/que_tex/1307.3716.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>\\nAccording to Theorem &lt;ref&gt;, ^d has exactly d...</td>\n",
       "      <td>Cyclicity classes</td>\n",
       "      <td>\\nAccording to Theorem &lt;ref&gt;, ^d has exactly d...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14916</th>\n",
       "      <td>Wielandt number</td>\n",
       "      <td>By {\\em Wielandt number} we mean the following...</td>\n",
       "      <td>/home/shufan/que_tex/1307.3716.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>By Wielandt number we mean the following funct...</td>\n",
       "      <td>Wielandt number</td>\n",
       "      <td>By B_MATH_TERM I_MATH_TERM we mean the followi...</td>\n",
       "      <td>O B_MATH_TERM I_MATH_TERM O O O O O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14917</th>\n",
       "      <td>Girth</td>\n",
       "      <td>\\label{d:girth}\\nThe {\\em girth\\/} of $\\digr$,...</td>\n",
       "      <td>/home/shufan/que_tex/1307.3716.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>\\nThe girth of , denoted it by g(),\\nis the sm...</td>\n",
       "      <td>Girth</td>\n",
       "      <td>\\nThe B_MATH_TERM of , denoted it by g(),\\nis ...</td>\n",
       "      <td>O B_MATH_TERM O O O O O O O O O O O O O O O O</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14918</th>\n",
       "      <td>Critical graph</td>\n",
       "      <td>\\label{d:crit}\\nLet $A\\in\\Rpnn$. The cycles of...</td>\n",
       "      <td>/home/shufan/que_tex/1307.3716.tex</td>\n",
       "      <td>definition[]</td>\n",
       "      <td>\\nLet A∈. The cycles of (A) at which the maxim...</td>\n",
       "      <td>Critical graph</td>\n",
       "      <td>\\nLet A∈. The cycles of (A) at which the maxim...</td>\n",
       "      <td>O O O O O O O O O O O O O O O O O O O O O O O ...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>14145 rows × 8 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                    term  \\\n",
       "0                                   admissible $G$-cover   \n",
       "1              light reduction pair;heavy reduction pair   \n",
       "2                                Local modification rule   \n",
       "3                                            Vertex sets   \n",
       "4                                               Palettes   \n",
       "...                                                  ...   \n",
       "14914  preferred direction;special claw corresponding...   \n",
       "14915                                  Cyclicity classes   \n",
       "14916                                    Wielandt number   \n",
       "14917                                              Girth   \n",
       "14918                                     Critical graph   \n",
       "\n",
       "                                                     def  \\\n",
       "0      \\label{def_admissibleGcover}\\nLet $G$ be a fin...   \n",
       "1      \\n  Let $\\pi\\in\\fs_n$ and let $x,y$ be a pair ...   \n",
       "2      \\label{lacma}  A \\emph{local modification rule...   \n",
       "3      \\label{vertset}  A \\emph{vertex set} is any se...   \n",
       "4      A \\emph{finite palette} is a sequence $K = (K_...   \n",
       "...                                                  ...   \n",
       "14914  \\label{definition:SpecialClaw} Consider $\\lang...   \n",
       "14915  \\label{d:cyclasses}\\nAccording to Theorem~\\ref...   \n",
       "14916  By {\\em Wielandt number} we mean the following...   \n",
       "14917  \\label{d:girth}\\nThe {\\em girth\\/} of $\\digr$,...   \n",
       "14918  \\label{d:crit}\\nLet $A\\in\\Rpnn$. The cycles of...   \n",
       "\n",
       "                                               file_name  \\\n",
       "0       /home/shufan/que_tex/abelian_tropical_covers.tex   \n",
       "1                    /home/shufan/que_tex/Post071005.tex   \n",
       "2             /home/shufan/que_tex/hereditary_submit.tex   \n",
       "3             /home/shufan/que_tex/hereditary_submit.tex   \n",
       "4             /home/shufan/que_tex/hereditary_submit.tex   \n",
       "...                                                  ...   \n",
       "14914  /home/shufan/que_tex/CosetsVoltagesAndDerivedE...   \n",
       "14915                 /home/shufan/que_tex/1307.3716.tex   \n",
       "14916                 /home/shufan/que_tex/1307.3716.tex   \n",
       "14917                 /home/shufan/que_tex/1307.3716.tex   \n",
       "14918                 /home/shufan/que_tex/1307.3716.tex   \n",
       "\n",
       "              extraction_rule  \\\n",
       "0        definition + \\emph{}   \n",
       "1        definition + \\emph{}   \n",
       "2                definition[]   \n",
       "3                definition[]   \n",
       "4                definition[]   \n",
       "...                       ...   \n",
       "14914  definition + \\textit{}   \n",
       "14915            definition[]   \n",
       "14916            definition[]   \n",
       "14917            definition[]   \n",
       "14918            definition[]   \n",
       "\n",
       "                                          plain_text_def  \\\n",
       "0      \\nLet G be a finite group and let X→ S be a fa...   \n",
       "1      \\n  Let π∈_n and let x,y be a pair of rooks th...   \n",
       "2        A local modification rule is a pair (A,T), w...   \n",
       "3        A vertex set is any set which is at most cou...   \n",
       "4      A finite palette is a sequence K = (K_j)_j=0^∞...   \n",
       "...                                                  ...   \n",
       "14914   Consider ⟨ G→ S, α→ A⟩, two adjacent vertices...   \n",
       "14915  \\nAccording to Theorem <ref>, ^d has exactly d...   \n",
       "14916  By Wielandt number we mean the following funct...   \n",
       "14917  \\nThe girth of , denoted it by g(),\\nis the sm...   \n",
       "14918  \\nLet A∈. The cycles of (A) at which the maxim...   \n",
       "\n",
       "                                         plain_text_term  \\\n",
       "0                                     admissible G-cover   \n",
       "1              light reduction pair;heavy reduction pair   \n",
       "2                                Local modification rule   \n",
       "3                                            Vertex sets   \n",
       "4                                               Palettes   \n",
       "...                                                  ...   \n",
       "14914  preferred direction;special claw corresponding...   \n",
       "14915                                  Cyclicity classes   \n",
       "14916                                    Wielandt number   \n",
       "14917                                              Girth   \n",
       "14918                                     Critical graph   \n",
       "\n",
       "                                   masked_plain_text_def  \\\n",
       "0      \\nLet G be a finite group and let X→ S be a fa...   \n",
       "1      \\n  Let π∈_n and let x,y be a pair of rooks th...   \n",
       "2        A B_MATH_TERM I_MATH_TERM I_MATH_TERM is a p...   \n",
       "3        A vertex set is any set which is at most cou...   \n",
       "4      A finite palette is a sequence K = (K_j)_j=0^∞...   \n",
       "...                                                  ...   \n",
       "14914   Consider ⟨ G→ S, α→ A⟩, two adjacent vertices...   \n",
       "14915  \\nAccording to Theorem <ref>, ^d has exactly d...   \n",
       "14916  By B_MATH_TERM I_MATH_TERM we mean the followi...   \n",
       "14917  \\nThe B_MATH_TERM of , denoted it by g(),\\nis ...   \n",
       "14918  \\nLet A∈. The cycles of (A) at which the maxim...   \n",
       "\n",
       "                                             labeled_def  \n",
       "0      O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "1      O O O O O O O O O O O O O O O O O O O O O O B_...  \n",
       "2      O B_MATH_TERM I_MATH_TERM I_MATH_TERM O O O O ...  \n",
       "3      O O O O O O O O O O O O O O O O B_MATH_TERM O ...  \n",
       "4      O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "...                                                  ...  \n",
       "14914  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "14915  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "14916  O B_MATH_TERM I_MATH_TERM O O O O O O O O O O O O  \n",
       "14917      O B_MATH_TERM O O O O O O O O O O O O O O O O  \n",
       "14918  O O O O O O O O O O O O O O O O O O O O O O O ...  \n",
       "\n",
       "[14145 rows x 8 columns]"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_clean = df_clean[~df_clean['diff_tokens']]\n",
    "df_clean = df_clean.drop(columns={'diff_tokens'})\n",
    "df_clean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "dccc3944-f951-4a2b-8d80-9cda9f7fd1cb",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_clean.to_csv(\"cleaned_plain-text_labeled_term+combined_no_ref_no_cit_def_same_len_only.csv\", index=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "2aa876c0-2203-460f-b1ac-63e8ba06d58e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "definition + \\emph{}      10360\n",
       "definition + \\textit{}     1775\n",
       "definition[]               1271\n",
       "theorem + \\emph{}           629\n",
       "theorem + \\textit{}         110\n",
       "Name: extraction_rule, dtype: int64"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_clean['extraction_rule'].value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "265bcb9f-045e-467a-95cf-b3e8722f08b1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "term                     0\n",
       "def                      0\n",
       "file_name                0\n",
       "extraction_rule          0\n",
       "plain_text_def           0\n",
       "plain_text_term          0\n",
       "masked_plain_text_def    0\n",
       "labeled_def              0\n",
       "diff_tokens              0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_clean['diff_tokens'] = df_clean.apply(lambda row: len(row['plain_text_def'].split()) != len(row['labeled_def'].split()), axis=1)\n",
    "df_clean[df_clean['diff_tokens']].count()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "96adda21-822b-4e86-b0ed-b31ef8dc8979",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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