Proceedings of the Japan Academy, Series A, Mathematical Sciences

On the growth rate of ideal Coxeter groups in hyperbolic 3-space

Yohei Komori and Tomoshige Yukita

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Abstract

We study the set $\mathcal{G}$ of growth rates of ideal Coxeter groups in hyperbolic 3-space; this set consists of real algebraic integers greater than 1. We show that (1) $\mathcal{G}$ is unbounded above while it has the minimum, (2) any element of $\mathcal{G}$ is a Perron number, and (3) growth rates of ideal Coxeter groups with $n$ generators are located in the closed interval $[n-3, n-1]$.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 91, Number 10 (2015), 155-159.

Dates
First available in Project Euclid: 2 December 2015

Permanent link to this document
https://projecteuclid.org/euclid.pja/1449080127

Digital Object Identifier
doi:10.3792/pjaa.91.155

Mathematical Reviews number (MathSciNet)
MR3430205

Zentralblatt MATH identifier
1336.20042

Subjects
Primary: 20F55: Reflection and Coxeter groups [See also 22E40, 51F15]
Secondary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]

Keywords
Coxeter group growth function growth rate Perron number

Citation

Komori, Yohei; Yukita, Tomoshige. On the growth rate of ideal Coxeter groups in hyperbolic 3-space. Proc. Japan Acad. Ser. A Math. Sci. 91 (2015), no. 10, 155--159. doi:10.3792/pjaa.91.155. https://projecteuclid.org/euclid.pja/1449080127


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