Jack polynomials and some identities for partitions

Abstract

We prove an identity about partitions involving new combinatorial coefficients. The proof given is using a generating function. As an application we obtain the explicit expression of two shifted symmetric functions, related with Jack polynomials. These quantities are the moments of the "alpha-content" random variable with respect to some transition probability distributions.

22 pages, LaTeX, to appear in Trans. Amer. Math. Soc