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

Tomoshige Yukita

Research output: Contribution to journal › Article

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

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Hyperbolic Groups
Coxeter Group
Dihedral angle
Polyhedron
Integer
Form

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Growth rates of 3-dimensional hyperbolic Coxeter groups are Perron numbers. / Yukita, Tomoshige.

In: Canadian Mathematical Bulletin, Vol. 61, No. 2, 01.06.2018, p. 405-422.

Research output: Contribution to journal › Article

Yukita, T 2018, 'Growth rates of 3-dimensional hyperbolic Coxeter groups are Perron numbers' Canadian Mathematical Bulletin, vol. 61, no. 2, pp. 405-422. https://doi.org/10.4153/CMB-2017-052-5
Yukita T. Growth rates of 3-dimensional hyperbolic Coxeter groups are Perron numbers. Canadian Mathematical Bulletin. 2018 Jun 1;61(2):405-422. https://doi.org/10.4153/CMB-2017-052-5
Yukita, Tomoshige. / Growth rates of 3-dimensional hyperbolic Coxeter groups are Perron numbers. In: Canadian Mathematical Bulletin. 2018 ; Vol. 61, No. 2. pp. 405-422.
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