Growth rates of 3-dimensional hyperbolic Coxeter groups are Perron\n numbers

2016/03/16 by Tomoshige Yukita, Yukita, Tomoshige
Computer Science · Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1603.04987

openalex publication_date 2016/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we consider the growth rates of 3-dimensional hyperbolic\nCoxeter polyhedra some of its dihedral angles are \(\π)/(m) for\nm\≥7. By combining with the classical result by Parry citePa and the\nmain result of citeY, we prove that the growth rates of 3-dimensional\nhyperbolic Coxeter groups are Perron numbers.\n

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