Growth of planar Coxeter groups, P.V.numbers and Salem numbers

DOI10.1007/BF01444729zbMath0735.51016OpenAlexW2079146090MaRDI QIDQ811511

William J. Floyd

Publication date: 1992

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/164970

zbMATH Keywords

Salem numbersCoxeter grouphyperbolic planereflectionsCoxeter systemgrowth exponentfinite sided polygongrowth of planar Coxeter groupsP. V. number

Mathematics Subject Classification ID

Reflection and Coxeter groups (group-theoretic aspects) (20F55) Polyhedra and polytopes; regular figures, division of spaces (51M20) PV-numbers and generalizations; other special algebraic numbers; Mahler measure (11R06)

Related Items (12)

Hyperbolic Coxeter groups of minimal growth rates in higher dimensions ⋮ Exponential growth rates of free and amalgamated products. ⋮ The growth rate and balance of homogeneous tilings in the hyperbolic plane ⋮ The growth rates for pure Artin groups of dihedral type. ⋮ Salem numbers, spectral radii and growth rates of hyperbolic Coxeter groups ⋮ On the growth of hyperbolic 3-dimensional generalized simplex reflection groups. ⋮ Cofinite hyperbolic Coxeter groups, minimal growth rate and Pisot numbers. ⋮ Deformation of finite-volume hyperbolic Coxeter polyhedra, limiting growth rates and Pisot numbers ⋮ Spherical and geodesic growth rates of right-angled Coxeter and Artin groups are Perron numbers ⋮ Hyperbolic Coxeter groups and minimal growth rates in dimensions four and five ⋮ On the growth rate of ideal Coxeter groups in hyperbolic 3-space. ⋮ On a structure of random open books and closed braids

Cites Work

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• Reciprocity of growth functions of Coxeter groups
• Growth functions of surface groups
• Symmetries of planar growth functions
• Growth series of Coxeter groups and Salem numbers
• Small Salem numbers
• On Poincaré's theorem for fundamental polygons
• Power series with integral coefficients
• Algebraic integers whose conjugates lie in the unit circle
• Ensembles fermés d'entiers algébriques
• Endomorphisms of linear algebraic groups
• Sur un ensemble fermé d'entiers algébriques

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