Abstract
This paper proves a combinatorial rule expressing the product s_tau (s_{lambda /mu } circ p_r) of a Schur function and the plethysm of a skew Schur function with a power-sum symmetric function as an integral linear combination of Schur functions. This generalizes the SXP rule for the plethysm s_lambda circ p_r. Each step in the proof uses either an explicit bijection or a sign-reversing involution. The proof is inspired by an earlier proof of the SXP rule due to Remmel and Shimozono (Discrete Math. 193:257–266, 1998). The connections with two later combinatorial rules for special cases of this plethysm are discussed. Two open problems are raised. The paper is intended to be readable by non-experts.
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