A weighted Murnaghan-Nakayama rule for (P, w)-partitions

2024/05/30 by Alexandersson, Per, Nabawanda, Olivia
#05E05 #05E10 #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2405.19932

Abstract

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.

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