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

Published online by Cambridge University Press:  20 November 2018

Tomoshige Yukita
Tomoshige Yukita*
Affiliation:
Department of Mathematics, School of Education, Waseda University, Nishi-Waseda 1-6-1, Shinjuku, Tokyo 169-8050, Japan, e-mail: yshigetomo@suou.waseda.jp
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Abstract

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In this paper we consider the growth rates of 3-dimensional hyperbolic Coxeter polyhedra with at least one dihedral angle of the form $\frac{\pi }{k}$ for an integer $k\ge 7$. 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.

Keywords

20F5520F65Coxeter groupgrowth functiongrowth ratePerron number
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 61 , Issue 2 , 01 June 2018 , pp. 405 - 422
Copyright
Copyright © Canadian Mathematical Society 2018

References

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