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Enriched $P$-Partitions

Author(s): John R. Stembridge
Journal: Trans. Amer. Math. Soc. 349 (1997), 763-788.
MSC (1991): Primary {06A07, 05E05}
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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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Additional Information:

John R. Stembridge
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109--1109

DOI: 10.1090/S0002-9947-97-01804-7
PII: S 0002-9947(97)01804-7
Received by editor(s): August 25, 1994
Additional Notes: Partially supported by NSF Grants DMS--9057192 and DMS--9401575
Copyright of article: Copyright 1997, American Mathematical Society

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