Enriched 𝑃-Partitions

Stembridge, John

doi:10.1090/S0002-9947-97-01804-7

Enriched $P$-Partitions
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by John R. Stembridge PDF

Trans. Amer. Math. Soc. 349 (1997), 763-788 Request permission

Abstract:

An (ordinary) $P$-partition is an order-preserving map from a partially ordered set to a chain, with special rules specifying where equal values may occur. Examples include number-theoretic partitions (ordered and unordered, strict or unrestricted), plane partitions, and the semistandard tableaux associated with Schur’s $S$-functions. In this paper, we introduce and develop a theory of enriched $P$-partitions; like ordinary $P$-partitions, these are order-preserving maps from posets to chains, but with different rules governing the occurrence of equal values. The principal examples of enriched $P$-partitions given here are the tableaux associated with Schur’s $Q$-functions. In a sequel to this paper, further applications related to commutation monoids and reduced words in Coxeter groups will be presented.

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