Growth functions for semi-regular tilings of the hyperbolic plane |
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Authors: | W J Floyd S P Plotnick |
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Institution: | (1) Department of Mathematics, VPI&SU, 24061-0123 Blacksburg, VA, USA;(2) Department of Mathematics, SUNY at Albany, 12222 Albany, NY, USA |
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Abstract: | This paper studies the growth function, with respect to the generating set of edge identifications, of a surface group with fundamental domainD in the hyperbolic plane ann-gon whose angles alternate between /p and /q. The possibilities ofn,p andq for which a torsion-free surface group can have such a fundamental polygon are classified, and the growth functions are computed. Conditions are given for which the denominator of the growth function is a product of cyclotomic polynomials and a Salem polynomial.This work was supported in part by NSF Research Grants. |
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Keywords: | Primary 20F32 secondary 22E40 20F05 57N05 |
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