Growth rates of Coxeter groups and Perron numbers

2019/12/11 by Kolpakov, Alexander, Talambutsa, Alexey
#11K16 #20F55 #37B10 #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1912.05608

Abstract

We define a large class of abstract Coxeter groups, that we call ∞--spanned, and for which the word growth rate and the geodesic growth rate appear to be Perron numbers. This class contains a fair amount of Coxeter groups acting on hyperbolic spaces, thus corroborating a conjecture by Kellerhals and Perren. We also show that for this class the geodesic growth rate strictly dominates the word growth rate.

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