A COMBINATORIAL PROOF OF A PLETHYSTIC MURNAGHAN-NAKAYAMA RULE

摘要

This article gives a short combinatorial proof of a plethystic generalization of the Murnaghan-Nakayama rule. The main result expresses the product of a Schur function with the plethysm p(r)oh(n) as an integral linear combination of Schur functions. The proof uses a sign-reversing involution on sequences of bead moves on James' abacus, inspired by the arguments in N.A. Loehr.