Proceedings of the Japan Academy, Series A, Mathematical Sciences

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

Yohei Komori and Yuriko Umemoto

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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.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 88, Number 4 (2012), 62-65.

First available in Project Euclid: 5 April 2012

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Zentralblatt MATH identifier

Primary: 20F55: Reflection and Coxeter groups [See also 22E40, 51F15]
Secondary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]

Growth function Coxeter group Perron number


Komori, Yohei; Umemoto, Yuriko. On the growth of hyperbolic 3-dimensional generalized simplex reflection groups. Proc. Japan Acad. Ser. A Math. Sci. 88 (2012), no. 4, 62--65. doi:10.3792/pjaa.88.62.

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