### 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 language | English |
---|---|

Pages (from-to) | 155-159 |

Number of pages | 5 |

Journal | Proceedings of the Japan Academy Series A: Mathematical Sciences |

Volume | 91 |

Issue number | 10 |

DOIs | |

Publication status | Published - 2015 |

### Fingerprint

### Keywords

- Coxeter group
- Growth function
- Growth rate
- Perron number

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**On the growth rate of ideal Coxeter groups in hyperbolic 3-space.** / Komori, Yohei; Yukita, Tomoshige.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - On the growth rate of ideal Coxeter groups in hyperbolic 3-space

AU - Komori, Yohei

AU - Yukita, Tomoshige

PY - 2015

Y1 - 2015

N2 - 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].

AB - 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].

KW - Coxeter group

KW - Growth function

KW - Growth rate

KW - Perron number

UR - http://www.scopus.com/inward/record.url?scp=84952323439&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84952323439&partnerID=8YFLogxK

U2 - 10.3792/pjaa.91.155

DO - 10.3792/pjaa.91.155

M3 - Article

VL - 91

SP - 155

EP - 159

JO - Proceedings of the Japan Academy Series A: Mathematical Sciences

JF - Proceedings of the Japan Academy Series A: Mathematical Sciences

SN - 0386-2194

IS - 10

ER -