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

教育学部

研究成果: Article › 査読

4 被引用数 (Scopus)

抄録

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].

本文言語	English
ページ（範囲）	155-159
ページ数	5
ジャーナル	Proceedings of the Japan Academy Series A: Mathematical Sciences
巻	91
号	10
DOI	https://doi.org/10.3792/pjaa.91.155
出版ステータス	Published - 2015

ASJC Scopus subject areas

数学 (全般)

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10.3792/pjaa.91.155

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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].

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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

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