Tokyo Journal of Mathematics

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

Ruth KELLERHALS and Jun NONAKA

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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.

Article information

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

Dates
First available in Project Euclid: 9 January 2018

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1515466832

Mathematical Reviews number (MathSciNet)
MR3743725

Zentralblatt MATH identifier
06855941

Subjects
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

Citation

NONAKA, Jun; KELLERHALS, Ruth. The Growth Rates of Ideal Coxeter Polyhedra in Hyperbolic 3-Space. Tokyo J. Math. 40 (2017), no. 2, 379--391. https://projecteuclid.org/euclid.tjm/1515466832


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