chapter  Chapter 11
30 Pages

Pólya Theory

WithRichard Klima, Neil Sigmon, Ernest Stitzinger

In this chapter, the authors present some results for counting equivalence classes when a group acts on a set. They deal with a discussion of why the Polya Enumeration Theorem is true. Rather than including a formal proof of the theorem, which would be complicated and not intuitive, the authors an informal discussion of why the theorem is true with two colors. They aim to count the number of patterns when a group acts on a set of colorings. Counting the number of orbits when a group acts on a set is the focus of a fundamental result due to W. Burnside. The authors show how Polya theory can be applied to the classification of switching functions.