Spherical and geodesic growth rates of right-angled Coxeter and Artin groups are Perron numbers

2018/09/25 by Kolpakov, Alexander, Talambutsa, Alexey · 1 citation
#Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1809.09591

Abstract

We prove that for any infinite right-angled Coxeter or Artin group, its spherical and geodesic growth rates (with respect to the standard generating set) either take values in the set of Perron numbers, or equal 1. Also, we compute the average number of geodesics representing an element of given word length in such groups.

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• Group word dynamics from local random matrix Hamiltonians and beyond

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