Growth functions for semi-regular tilings of the hyperbolic plane
type: Item
instance of: scholarly article
title: Growth functions for semi-regular tilings of the hyperbolic plane
zbMATH Open document ID: 0820.57012
DOI: 10.1007/BF01264041
published in: Geometriae Dedicata
publication date: 1995-09-14T00:00:00Z
review text: Cannon and Wagreich computed the growth function of a genus \(g\) surface group with fundamental domain a \(4g\)-gon. In the paper under review the authors study the growth function, with respect to the generating set of edge identifications, of a surface group with fundamental domain \(D\) in the hyperbolic plane an \((n; p,q)\)-gon; i.e., vertices of \(D\) have angle measures that alternate between \({{2\pi} \over p}\) and \({{2\pi} \over q}\) for some integers \(p,q\geq 3\). After classifying the values of \(n\), \(p\), \(q\) for which there is a torsion-free surface group with fundamental polygon an \((n; p,q)\)-gon, the growth functions \(f\) are computed. Finally conditions are given for the denominator of \(f\) to be a product of a Salem polynomial and cyclotomic polynomials.
Mathematics Subject Classification ID: 57M60
Mathematics Subject Classification ID: 20F65
zbMATH DE Number: 701140
zbMATH Keywords: growth function
zbMATH Keywords: edge identifications
zbMATH Keywords: surface group
zbMATH Keywords: fundamental domain
author: William Floyd
author: Steven P. Plotnick
reviewed by: Wolfgang Heil
MaRDI profile type: Publication
cites work: The combinatorial structure of cocompact discrete hyperbolic groups
cites work: Growth functions on Fuchsian groups and the Euler characteristic
cites work: Symmetries of planar growth functions
cites work: Q4750850
full work available at URL: https://doi.org/10.1007/bf01264041
OpenAlex ID: W2035689494
description: scientific article; zbMATH DE number 701140