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

Tomoshige Yukita

doi:10.4153/CMB-2017-052-5

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

Tomoshige Yukita^*

^*Corresponding author for this work

School of Education

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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 language	English
Pages (from-to)	405-422
Number of pages	18
Journal	Canadian Mathematical Bulletin
Volume	61
Issue number	2
DOIs	https://doi.org/10.4153/CMB-2017-052-5
Publication status	Published - 2018 Jun

Keywords

Coxeter group
Growth function
Growth rate
Perron number

ASJC Scopus subject areas

Mathematics(all)

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10.4153/CMB-2017-052-5

Cite this

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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.",

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AB - 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.

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KW - Growth function

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KW - Perron number

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

Abstract

Keywords

ASJC Scopus subject areas

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