Pólya enumeration theorem

The Pólya enumeration theorem, also known as the Redfield–Pólya theorem and Pólya counting, is a theorem in combinatorics that both follows from and ultimately generalizes Burnside's lemma on the number of orbits of a group action on a set. The theorem was first published by J. Howard Redfield in 1927. In 1937 it was independently rediscovered by George Pólya, who then greatly popularized the result by applying it to many counting problems, in particular to the enumeration of chemical compounds.

"Polya theorem" redirects here. For Pólya's theorem for positive polynomials on simplex, see Positive polynomial. For the recurrence of lattice random walks, see Random walk § Higher dimensions.

The Pólya enumeration theorem has been incorporated into symbolic combinatorics and the theory of combinatorial species.

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.