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

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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].

Original languageEnglish
Pages (from-to)155-159
Number of pages5
JournalProceedings of the Japan Academy Series A: Mathematical Sciences
Volume91
Issue number10
DOIs
Publication statusPublished - 2015

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Keywords

  • Coxeter group
  • Growth function
  • Growth rate
  • Perron number

ASJC Scopus subject areas

  • Mathematics(all)

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