Generating Functions for Hyperbolic Plane Tessellations

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Date

2017-08-28

Authors

Xie, Jiale

Advisor

Wagner, David

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University of Waterloo

Abstract

For a hyperbolic plane tessellation there is a generating function with respect to the distance. This generating function is the same as the growth function of a group of isometries of hyperbolic plane that acts regularly in the tessellation. For most of the tessellation the generating functions have a symmetric form. In this thesis we will show the computation of the generating function for the hyperbolic plane tessellation and find the tessellations that have a symmetric form in the generating functions.

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