Growth Rates of 3-dimensional Hyperbolic Coxeter Groups are Perron Numbers

Abstract

AbstractIn this paper we consider the growth rates of 3-dimensional hyperbolic Coxeter polyhedra with at least one dihedral angle of the formfor an integer k ≥ 7. Combining a classical result by Parry with a previous result of ours, we prove that the growth rates of 3-dimensional hyperbolic Coxeter groups are Perron numbers.