A counterexample to a Brenti-Carnevale conjecture

TL;DR

This paper presents a counterexample to a conjecture by Brenti on Coxeter groups and unimodality, challenging previous assumptions and providing data to guide future research in this area.

Contribution

It offers the first known counterexample to the Brenti-Carnevale conjecture and supplies supporting data, advancing understanding of Coxeter groups and unimodality.

Findings

Counterexample refutes the conjecture

Supporting data illustrates the counterexample

Initial step for further exploration

Abstract

Recently, F. Brenti put a preprint on the arXiv with several interesting open problems on Coxeter groups and unimodality. In this note, we refute one of these conjectures with a counterexample and provide supporting data related to it. This work serves as an initial step toward further exploration of the topic.