Geodesic growth in right-angled and even Coxeter groups

TL;DR

This paper investigates how combinatorial properties of regular graphs influence the geodesic growth of associated right-angled and even Coxeter groups, providing new examples of groups with identical growth series.

Contribution

It identifies graph properties that determine geodesic growth and presents the first examples of different Coxeter groups sharing the same growth series.

Findings

Certain graph properties fully determine geodesic growth.

First known examples of distinct Coxeter groups with identical growth series.

Establishes connections between graph combinatorics and group growth behavior.

Abstract

The objective of this paper is to detect which combinatorial properties of a regular graph can completely determine the geodesic growth of the right-angled Coxeter or Artin group this graph defines, and to provide the first examples of right-angled and even Coxeter groups with the same geodesic growth series.