The combinatorics of rim hook tableaux

We give a new combinatorial proof that the coefficient of the power symmetric function p(mu) in the Schur symmetric function s(lambda) can be expressed in terms of rim hook tableaux (the Murnaghan-Nakayama rule). Two other known identities involving the coefficient of p(mu) in the homogeneous symmetric function h(lambda) and the coefficient of p(mu) in the elementary symmetric function e(lambda) are proved in similar ways.