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

Published:2017-12-05

• Tomoshige Yukita,
Department of Mathematics, School of Education, Waseda University, Tokyo, Japan
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## Abstract

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 $k\geq{7}$. 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: Coxeter group, growth function, growth rate, Perron number