Open Access
Translator Disclaimer
December 2015 On the growth rate of ideal Coxeter groups in hyperbolic 3-space
Yohei Komori, Tomoshige Yukita
Proc. Japan Acad. Ser. A Math. Sci. 91(10): 155-159 (December 2015). DOI: 10.3792/pjaa.91.155

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 $[n-3, n-1]$.

Citation

Download Citation

Yohei Komori. Tomoshige Yukita. "On the growth rate of ideal Coxeter groups in hyperbolic 3-space." Proc. Japan Acad. Ser. A Math. Sci. 91 (10) 155 - 159, December 2015. https://doi.org/10.3792/pjaa.91.155

Information

Published: December 2015
First available in Project Euclid: 2 December 2015

zbMATH: 1336.20042
MathSciNet: MR3430205
Digital Object Identifier: 10.3792/pjaa.91.155

Subjects:
Primary: 20F55
Secondary: 20F65

Keywords: Coxeter group , growth function , Growth rate , Perron number

Rights: Copyright © 2015 The Japan Academy

JOURNAL ARTICLE
5 PAGES


SHARE
Vol.91 • No. 10 • December 2015
Back to Top