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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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