  This article gives a combinatorial proof of a plethystic generalization of
the Murnaghan--Nakayama rule. The main result expresses the product of a Schur
function with the plethysm $p_r \circ h_n$ 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. Loehr, Abacus
proofs of Schur function identities, SIAM J. Discrete Math. 24 (2010),
1356-1370.
