Applications and Analysis of Burnside's Theorem
Kristen Walcott. Applications and Analysis of Burnside's Theorem. Department of Mathematics, Allegheny College. May 2005.
Abstract
Some counting problems are simple enough to solve by observation, but many require a more sophisticated approach. Burnside's Theorem is a result of group theory that is often used to calculate the number of nonequivalent arrangements of colorings of objects in a set under a group of permutations. In this project, we will discuss the notion of an arbitrary group acting on a set, the analysis and several applications of Burnside's Theorem, and a generalization of the theorem.
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