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 π/p and π/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.
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This work was supported in part by NSF Research Grants.
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Floyd, W.J., Plotnick, S.P. Growth functions for semi-regular tilings of the hyperbolic plane. Geom Dedicata 53, 1–23 (1994). https://doi.org/10.1007/BF01264041
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DOI: https://doi.org/10.1007/BF01264041