Deformation of finite-volume hyperbolic Coxeter polyhedra, limiting growth rates and Pisot numbers

2011/05/31 by Alexander Kolpakov, Kolpakov, Alexander · 1 citation
Computer Science · Mathematics · #11K16 #20F55 #52B10 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Metric Geometry (math.MG) #semigroups and automata theory

paper · doi:10.48550/arxiv.1105.6267

openalex publication_date 2011/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A connection between real poles of the growth functions for Coxeter groups acting on hyperbolic space of dimensions three and greater and algebraic integers is investigated. In particular, a geometric convergence of fundamental domains for cocompact hyperbolic Coxeter groups with finite-volume limiting polyhedron provides a relation between Salem numbers and Pisot numbers. Several examples conclude this work.

Cited by

• Random walks on cocompact Fuchsian and Kleinian groups

Related

• Salem numbers, spectral radii and growth rates of hyperbolic Coxeter groups
• Hyperbolic Coxeter groups of minimal growth rates in higher dimensions
• On the continuity of the growth rate on the space of Coxeter systems
• Growth rates of 3-dimensional hyperbolic Coxeter groups are Perron\n numbers
• On 3-dimensional hyperbolic Coxeter pyramids