  The $(P, w)$-partition generating function $K_{(P,w)}(x)$ is a quasisymmetric
function obtained from a labeled poset. Recently, Liu and Weselcouch gave a
formula for the coefficients of $K_{(P,w)}(x)$ when expanded in the
quasisymmetric power sum function basis. This formula generalizes the classical
Murnaghan--Nakayama rule for Schur functions.
  We extend this result to weighted $(P, w)$-partitions and provide a short
combinatorial proof, avoiding the Hopf algebra machinery used by
Liu-Weselcouch.
