Growth rates of 3-dimensional hyperbolic Coxeter groups are Perron numbers

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Abstract

In this paper we consider the growth rates of 3-dimensional hyperbolic Coxeter polyhedra with at least one dihedral angle of the form π/k for an integer k ≥ 7. Combining a classical result by Parry with a previous result of ours, we prove that the growth rates of 3-dimensional hyperbolic Coxeter groups are Perron numbers.

Original languageEnglish
Pages (from-to)405-422
Number of pages18
JournalCanadian Mathematical Bulletin
Volume61
Issue number2
DOIs
Publication statusPublished - 2018 Jun 1

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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