DECOMPOSITION OF CERTAIN PRODUCTS OF CONJUGACY CLASSES OF S(N)

Using the character theory of the symmetric group S(n), we study the d ecomposition of the product of two conjugacy classes K(lambda) K(mu) in the basis of conjugacy classes. This product takes place in the gr oup algebra of the symmetric group, and the coefficient of the class K (gamma) in the decomposition, called structure constant, is a positive integer that counts the number of ways of writing a given permutation of type gamma as a product of two permutations of type lambda and mu. In this paper, we present new formulas for the decomposition of the p roducts K1rn-r K1sn-s and K(r,n-r) * K(s,n-s) over a restricted set of conjugacy classes K(gamma). These formulas generalize the formula f or the decomposition of the product of the class of full cycles with i tself K(n) K(n). (C) 1994 Academic Press, Inc.