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

Yohei Komori; Tomoshige Yukita

doi:10.3792/pjaa.91.155

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

Yohei Komori, Tomoshige Yukita

School of Education

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

We study the set 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) G is unbounded above while it has the minimum, (2) any element of 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].

Original language	English
Pages (from-to)	155-159
Number of pages	5
Journal	Proceedings of the Japan Academy Series A: Mathematical Sciences
Volume	91
Issue number	10
DOIs	https://doi.org/10.3792/pjaa.91.155
Publication status	Published - 2015

Keywords

Coxeter group
Growth function
Growth rate
Perron number

ASJC Scopus subject areas

Mathematics(all)

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10.3792/pjaa.91.155

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abstract = "We study the set 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) G is unbounded above while it has the minimum, (2) any element of 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].",

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AU - Yukita, Tomoshige

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AB - We study the set 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) G is unbounded above while it has the minimum, (2) any element of 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].

KW - Coxeter group

KW - Growth function

KW - Growth rate

KW - Perron number

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

Abstract

Keywords

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