Tokyo Journal of Mathematics

The Growth Rates of Ideal Coxeter Polyhedra in Hyperbolic 3-Space


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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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Tokyo J. Math., Volume 40, Number 2 (2017), 379-391.

First available in Project Euclid: 9 January 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F55: Reflection and Coxeter groups [See also 22E40, 51F15]
Secondary: 51F15: Reflection groups, reflection geometries [See also 20H10, 20H15; for Coxeter groups, see 20F55] 52B10: Three-dimensional polytopes


NONAKA, Jun; KELLERHALS, Ruth. The Growth Rates of Ideal Coxeter Polyhedra in Hyperbolic 3-Space. Tokyo J. Math. 40 (2017), no. 2, 379--391.

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