On the growth of hyperbolic 3-dimensional generalized simplex reflection groups

Yohei Komori; Yuriko Umemoto

doi:10.3792/pjaa.88.62

On the growth of hyperbolic 3-dimensional generalized simplex reflection groups

Yohei Komori^*, Yuriko Umemoto

^*Corresponding author for this work

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

6 Citations (Scopus)

Abstract

We prove that the growth rates of three-dimensional generalized simplex reflection groups, i.e. three-dimensional non-compact hyperbolic Coxeter groups with four generators are always Perron numbers.

Original language	English
Pages (from-to)	62-65
Number of pages	4
Journal	Proceedings of the Japan Academy Series A: Mathematical Sciences
Volume	88
Issue number	4
DOIs	https://doi.org/10.3792/pjaa.88.62
Publication status	Published - 2012
Externally published	Yes

Keywords

Coxeter group
Growth function
Perron number

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.3792/pjaa.88.62

Cite this

@article{035382bfacec433ea7e31b53d389172b,

title = "On the growth of hyperbolic 3-dimensional generalized simplex reflection groups",

abstract = "We prove that the growth rates of three-dimensional generalized simplex reflection groups, i.e. three-dimensional non-compact hyperbolic Coxeter groups with four generators are always Perron numbers.",

keywords = "Coxeter group, Growth function, Perron number",

author = "Yohei Komori and Yuriko Umemoto",

year = "2012",

doi = "10.3792/pjaa.88.62",

language = "English",

volume = "88",

pages = "62--65",

journal = "Proceedings of the Japan Academy Series A: Mathematical Sciences",

issn = "0386-2194",

publisher = "Japan Academy",

number = "4",

}

TY - JOUR

T1 - On the growth of hyperbolic 3-dimensional generalized simplex reflection groups

AU - Komori, Yohei

AU - Umemoto, Yuriko

PY - 2012

Y1 - 2012

N2 - We prove that the growth rates of three-dimensional generalized simplex reflection groups, i.e. three-dimensional non-compact hyperbolic Coxeter groups with four generators are always Perron numbers.

AB - We prove that the growth rates of three-dimensional generalized simplex reflection groups, i.e. three-dimensional non-compact hyperbolic Coxeter groups with four generators are always Perron numbers.

KW - Coxeter group

KW - Growth function

KW - Perron number

UR - http://www.scopus.com/inward/record.url?scp=84862977103&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84862977103&partnerID=8YFLogxK

U2 - 10.3792/pjaa.88.62

DO - 10.3792/pjaa.88.62

M3 - Article

AN - SCOPUS:84862977103

SN - 0386-2194

VL - 88

SP - 62

EP - 65

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

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

IS - 4

ER -

On the growth of hyperbolic 3-dimensional generalized simplex reflection groups

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this