Enriched -Partitions

Author:
John R. Stembridge

Journal:
Trans. Amer. Math. Soc. **349** (1997), 763-788

MSC (1991):
Primary {06A07, 05E05}

DOI:
https://doi.org/10.1090/S0002-9947-97-01804-7

MathSciNet review:
1389788

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Abstract | References | Similar Articles | Additional Information

Abstract: An (ordinary) -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 -functions. In this paper, we introduce and develop a theory of enriched -partitions; like ordinary -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 -partitions given here are the tableaux associated with Schur's -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:
https://doi.org/10.1090/S0002-9947-97-01804-7

Received by editor(s):
August 25, 1994

Additional Notes:
Partially supported by NSF Grants DMS–9057192 and DMS–9401575

Article copyright:
© Copyright 1997
American Mathematical Society