Some open problems on Coxeter groups and unimodality

TL;DR

This paper discusses open problems related to Coxeter groups and unimodality, presenting partial results and computational evidence to advance understanding in these mathematical areas.

Contribution

It introduces new open problems on Coxeter groups and unimodality, along with partial results and computational data that shed light on these issues.

Findings

Partial results on Coxeter groups and unimodality

Computational evidence supporting certain conjectures

Identification of key open problems in the field

Abstract

In this paper I present some open problems on Coxeter groups and unimodality, together with the main partial results, and computational evidence, that are known about them.