Master of Science (MS)
First Committee Member
Number of Pages
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.
Average; Cayley; Dihedral; Genus; Groups; Maps
University of Nevada, Las Vegas
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Langille, Jamie Keith, "Average Cayley genus for Cayley maps with dihedral groups" (2000). UNLV Retrospective Theses & Dissertations. 1214.