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arXiv · 1903.00551

$P$-Partitions and Quasisymmetric Power Sums

Ricky Ini Liu·Michael Weselcouch
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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.

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Ricky Ini Liu, Michael Weselcouch. 2019-03-01. $P$-Partitions and Quasisymmetric Power Sums. https://arxiv.org/abs/1903.00551

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