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arXiv · 1603.04987

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

Tomoshige Yukita
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Abstract

In this paper we consider the growth rates of 3-dimensional hyperbolic Coxeter polyhedra some of its dihedral angles are $\fracπ{m}$ for $m\geq{7}$. By combining with the classical result by Parry \cite{Pa} and the main result of \cite{Y}, we prove that the growth rates of 3-dimensional hyperbolic Coxeter groups are Perron numbers.

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Tomoshige Yukita. 2017-05-07. Growth rates of 3-dimensional hyperbolic Coxeter groups are Perron numbers. https://arxiv.org/abs/1603.04987

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