A weighted Murnaghan-Nakayama rule for $(P, w)$-partitions
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866915800140480512 |
|---|---|
| author | Alexandersson, Per Nabawanda, Olivia |
| author_facet | Alexandersson, Per Nabawanda, Olivia |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19932 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A weighted Murnaghan-Nakayama rule for $(P, w)$-partitions Alexandersson, Per Nabawanda, Olivia Combinatorics Representation Theory 05E10, 05E05 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. |
| title | A weighted Murnaghan-Nakayama rule for $(P, w)$-partitions |
| topic | Combinatorics Representation Theory 05E10, 05E05 |
| url | https://arxiv.org/abs/2405.19932 |