Symmetries of planar growth functions

DOI10.1007/BF01410198zbMath0652.20052OpenAlexW2165839278MaRDI QIDQ1106951

Steven P. Plotnick, William J. Floyd

Publication date: 1988

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143607

zbMATH Keywords

wordsgeneratorsgrowth functionfinitely generated groupfinite generating setEuclidean and Hyperbolic planar isometry groupsgeometric generating setsgeometrically defined groupsirreducible Euclidean Coxeter group

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10)

Related Items

Growth functions for semi-regular tilings of the hyperbolic plane, The growth rate and balance of homogeneous tilings in the hyperbolic plane, The arithmetic and geometry of Salem numbers, On problems related to growth, entropy, and spectrum in group theory, Symmetries of Planar Growth Functions. II, Constructions of Pisot and Salem numbers with flat palindromes, Growth series for the group \(\langle x,y\mid x^{-1}yx=y^ l\rangle\), Growth of planar Coxeter groups, P.V.numbers and Salem numbers

Cites Work

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• Groups generated by reflections and aspherical manifolds not covered by Euclidean space
• The combinatorial structure of cocompact discrete hyperbolic groups
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• Growth functions for semi-regular tilings of the hyperbolic plane
• On Poincaré's theorem for fundamental polygons
• Endomorphisms of linear algebraic groups