On products of conjugacy classes of the symmetric group

Abstract The product of conjugacy classes of the symmetric group in its group algebra is found as a linear combination of conjugacy classes with integer coefficients. The purpose of this paper is to give a partial answer to the problem of finding simple combinatorial rules to obtain these coefficients. In particular, we will show that the product C (n) ∗C (n) of the class of circular permutations with itself can be decomposed in a simple manner.