Ricci curvature, Bruhat graphs and Coxeter groups
Combinatorics
2021-02-25 v2 Group Theory
Abstract
We consider the notion of discrete Ricci curvature for graphs defined by Schmuckenschl{\"a}ger \cite{shmuck} and compute its value for Bruhat graphs associated to finite Coxeter groups. To do so we work with the geometric realization of a finite Coxeter group and a classical result obtained by Dyer in \cite{Dyer}. As an application we obtain a bound for the spectral gap of the Bruhat graph of any finite Coxeter group and an isoperimetric inequality for them. Our proofs are case-free.
Cite
@article{arxiv.2102.11277,
title = {Ricci curvature, Bruhat graphs and Coxeter groups},
author = {Viola Siconolfi},
journal= {arXiv preprint arXiv:2102.11277},
year = {2021}
}
Comments
12 pages. arXiv admin note: text overlap with arXiv:2102.10134