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- Title
P-Partitions and Quasisymmetric Power Sums.
- Authors
Liu, Ricky Ini; Weselcouch, Michael
- Abstract
The |$(P, \omega)$| -partition generating function of a labeled poset |$(P, \omega)$| is a quasisymmetric function enumerating certain order-preserving maps from |$P$| to |${\mathbb{Z}}^+$|. We study the expansion of this generating function in the recently introduced type 1 quasisymmetric power sum basis |$\{\psi _{\alpha }\}$|. Using this expansion, we show that connected, naturally labeled posets have irreducible |$P$| -partition generating functions. We also show that series-parallel posets are uniquely determined by their partition generating functions. We conclude by giving a combinatorial interpretation for the coefficients of the |$\psi _{\alpha }$| -expansion of the |$(P, \omega)$| -partition generating function akin to the Murnaghan–Nakayama rule.
- Subjects
GENERATING functions; PARTITION functions; PARTIALLY ordered sets
- Publication
IMRN: International Mathematics Research Notices, 2021, Vol 2021, Issue 18, p13975
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnz375