A weighted Murnaghan–Nakayama rule for ( P , ω ) -partitions
Abstract
The ( P , ω ) -partition generating function K ( P , ω ) ( x ) is a quasisymmetric function obtained from a labeled poset. Recently, Liu and Weselcouch gave a formula for the coefficients of K ( P , ω ) ( 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 , ω ) -partitions and provide a short combinatorial proof, avoiding the Hopf algebra machinery used by Liu–Weselcouch.
Fields of Study & Subjects
Advanced Mathematical Identities
Mathematical Inequalities and Applications
Analytic Number Theory Research
Publication details
- Journal / source
- European Journal of Combinatorics
- Publisher
- Elsevier BV
- Volume
- 134
- Pages
- 104332–104332
- Publication date
- 12 January 2026
- Language
- EN