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

Permissions

If you are the rightful copyright holder of this dissertation or thesis and wish to have the full text removed from Digital Scholarship@UNLV, please submit a request to digitalscholarship@unlv.edu and include clear identification of the work, preferably with URL.

Identifier

https://doi.org/10.25669/ezxp-f1u0


Share

COinS