Permanent conjectures

[benoitseron]

At this stage I really feel that this is where we can have added value: our recent article with Nicolas and Leo, as well as another one in preparation, is around the mathematics of (broken or not) permanent conjectures, as found in https://arxiv.org/abs/1608.02844.

I believe that for most of those conjectures we can find interesting stuff to say, they are quite obviously linked to physics.

Oddly enough, little numerical work has been done on the matter. This could in fact be a full fledged article, especially if we find new, interesting counter examples.

[benoitseron]

Of course, this is where we can bring something, rather than just a few permanent functions. We must do an intelligent search for counter examples, and a HPC package that we will run on clusters.

[benoitseron]

It will be a few thousand lines (mostly easy ones). I don't know to what extent just a direct numerical search without new interesting counter examples can be used an article proper (at a regime above JOSS). I do have new counter examples but they are not that interesting.