Growth rates of Coxeter groups and Perron numbers

Abstract

We define a large class of abstract Coxeter groups, which we call ∞spanned, 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 partially confirming a conjecture by Kellerhals and Perren.We also show that for this class the geodesic growth rate strictly dominates the word growth rate.