Title

Growth of tessellations

Date of Award

2009

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

Advisor(s)

Mark E. Watkins

Keywords

Tessellations, Growth rate, Hyperbolic plane, Homogeneous

Subject Categories

Physical Sciences and Mathematics

Abstract

A tessellation is understood to be a 1-ended, locally finite, locally cofinite, 3-connected planar map. A definition for the rate of exponential growth of a tessellation of the hyperbolic plane is established, and existing methods for computing growth are refined. Growth rates of both face- and edge-homogeneous tessellations are considered, and two major results are proven: first, that tessellations exist for any arbitrary growth rate greater than or equal to 1, and second, that the least rate of growth for a face-homogeneous tessellation is (1 + [Special characters omitted.] )/2.

Comments

ISBN 9781109463040

Access

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