A recursion of the Polya polynomial for the symmetric group

摘要

A recursion for the Polya polynomial of the symmetric group is proved. This recursion will be used to compute the Polya polynomial of the Young group. In turn, a theorem by George Polya, generalized by deBruijn, will be used to compute the double cosets of Young groups embedded in an overall symmetric group. Connections to mathematical physics and combinatorics will be noted but not proved.