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

DOI10.3792/pjaa.88.62zbMath1244.20039arXiv1503.00583OpenAlexW2087424920MaRDI QIDQ431736

Yohei Komori, Yuriko Umemoto

Publication date: 30 June 2012

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.00583

zbMATH Keywords

generating setsgrowth rateCoxeter groupgrowth functionsgrowth functionlength functionshyperbolic Coxeter groupsPerron numbersPerron number

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Hyperbolic groups and nonpositively curved groups (20F67)

Related Items (6)

The growth rates for pure Artin groups of dihedral type. ⋮ On the growth of hyperbolic 3-dimensional generalized simplex reflection groups. ⋮ Cofinite hyperbolic Coxeter groups, minimal growth rate and Pisot numbers. ⋮ The growth rates of ideal Coxeter polyhedra in hyperbolic 3-space ⋮ Seventy years of Salem numbers ⋮ On the growth rate of ideal Coxeter groups in hyperbolic 3-space.

Cites Work

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• On the growth of hyperbolic 3-dimensional generalized simplex reflection groups.
• On the growth of cocompact hyperbolic Coxeter groups.
• Growth functions of surface groups
• Growth of planar Coxeter groups, P.V.numbers and Salem numbers
• Groupes de Coxeter infinis non affines. (Infinite non affine Coxeter groups)
• Growth series of Coxeter groups and Salem numbers
• The volume of hyperbolic Coxeter polytopes of even dimension
• The orders of the finite Chevalley groups
• Endomorphisms of linear algebraic groups

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