An extension of Burnside's lemma is presented along with its suggested implementation in computer code. The extension is along the lines of de Bruijn's work, which itself is a generalization of Polya's theory of counting. As an example, in addition to counting the number of distinguishable colorings of a checkerboard if rotations and reflections are allowed, our extension allows the colors themselves to be permuted. The historical context is briefly discussed. Examples are given along the way to illuminate the discussion.

Author Bio

Lucas Wagner is a mathematics and physics double major, having graduated in May 2008 from Concordia College in Moorhead, MN. Lucas grew up in Fargo, ND, but he plans to move out to California this fall for graduate school in physics at UC Irvine. His hobbies include piano playing and computer programming; the latter helped him further explore Burnside's lemma. Dr. Dan Biebighauser of Concordia College taught an advanced Modern Algebra course, which brought up the lemma. Lucas is thankful to Dr. Biebighauser for his support in the writing of this paper.