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December 2017 The Growth Rates of Ideal Coxeter Polyhedra in Hyperbolic 3-Space
Ruth KELLERHALS, Jun NONAKA
Tokyo J. Math. 40(2): 379-391 (December 2017). DOI: 10.3836/tjm/1502179234

Abstract

In~[7], Kellerhals and Perren conjectured that the growth rates of the reflection groups given by compact hyperbolic Coxeter polyhedra are always Perron numbers. We prove that this conjecture holds in the context of ideal Coxeter polyhedra in $\mathbb{H}^3$. Our methods allow us to bound from below the growth rates of composite ideal Coxeter polyhedra by the growth rates of its ideal Coxeter polyhedral constituents.

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Ruth KELLERHALS. Jun NONAKA. "The Growth Rates of Ideal Coxeter Polyhedra in Hyperbolic 3-Space." Tokyo J. Math. 40 (2) 379 - 391, December 2017. https://doi.org/10.3836/tjm/1502179234

Information

Published: December 2017
First available in Project Euclid: 9 January 2018

zbMATH: 06855941
MathSciNet: MR3743725
Digital Object Identifier: 10.3836/tjm/1502179234

Subjects:
Primary: 20F55
Secondary: 51F15, 52B10

Rights: Copyright © 2017 Publication Committee for the Tokyo Journal of Mathematics

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Vol.40 • No. 2 • December 2017
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