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Growth Rates of 3-dimensional Hyperbolic Coxeter Groups are Perron Numbers
Published online by Cambridge University Press: 20 November 2018
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
$k\ge 7$. 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.
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- Copyright © Canadian Mathematical Society 2018
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