Growth rates of Coxeter groups and Perron numbers
Abstract
We define a large class of abstract Coxeter groups, that we call $\infty$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.
 Publication:

arXiv eprints
 Pub Date:
 December 2019
 arXiv:
 arXiv:1912.05608
 Bibcode:
 2019arXiv191205608K
 Keywords:

 Mathematics  Group Theory;
 Mathematics  Combinatorics;
 Mathematics  Geometric Topology;
 Mathematics  Number Theory;
 20F55;
 37B10;
 11K16
 EPrint:
 21 pages, 2 figures