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Séminaire Lotharingien de Combinatoire, 80B.73 (2018), 12 pp.

# Ricky Ini Liu and Michael Weselcouch

*P*-Partition Generating Function Equivalence of Naturally Labeled Posets

**Abstract.**
The *P-partition generating function* of a (naturally labeled)
poset *P* is a quasisymmetric function enumerating order-preserving
maps from *P* to **Z**^{+}. Using the Hopf algebra of posets, we give
necessary conditions for two posets to have the same generating
function. In particular, we show that they must have the same number
of antichains of each size and the same shape (as defined by
Greene). We also discuss which shapes guarantee uniqueness of the
*P*-partition generating function and give a method of constructing
pairs of non-isomorphic posets with the same generating function.

Received: November 14, 2017.
Accepted: February 17, 2018.
Final version: April 1, 2018.

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