Award Date

1-1-2000

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematical Sciences

First Committee Member

Michelle Schultz

Number of Pages

52

Abstract

Let Gamma be a finite group and let Delta be a generating set for Gamma. A Cayley map associated with Gamma and Delta is an oriented 2-cell embedding of the Cayley graph GDelta (Gamma) such that the rotation of arcs emanating from each vertex is determined by a unique cyclic permutation of generators and their inverses. A formula for the average Cayley genus is known for the dihedral group with generating set consisting of all the reflections. However, the known formula involves sums of certain coefficients of a generating function and its format does not specifically indicate the Cayley genus distribution. We determine a simplified formula for this average Cayley genus as well as provide improved understanding of the Cayley genus distribution.

Keywords

Average; Cayley; Dihedral; Genus; Groups; Maps

Controlled Subject

Mathematics

File Format

pdf

File Size

1382.4 KB

Degree Grantor

University of Nevada, Las Vegas

Language

English

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