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Extensions Of The Power Group Enumeration Theorem, Shawn Jeffrey Green

Theses and Dissertations

The goal of this paper is to develop extensions of Polya enumeration methods which count orbits of functions. De Bruijn, Harary, and Palmer all worked on this problem and created generalizations which involve permuting the codomain and domain of functions simultaneously. We cover their results and specifically extend them to the case where the group of permutations need not be a direct product of groups. In this situation, we develop a way of breaking the orbits into subclasses based on a characteristic of the functions involved. Additionally, we develop a formula for the number of orbits made up of bijective …