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.
Daniel P. Biebighauser
"Beyond Burnside's Lemma,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 9:
2, Article 8.
Available at: https://scholar.rose-hulman.edu/rhumj/vol9/iss2/8