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Enriched $P$-Partitions.
- Source :
-
Transactions of the American Mathematical Society . Feb1997, Vol. 349 Issue 2, p763-788. 26p. - Publication Year :
- 1997
-
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. } [ABSTRACT FROM AUTHOR]
- Subjects :
- *PARTITIONS (Mathematics)
*ALGEBRA
Subjects
Details
- Language :
- English
- ISSN :
- 00029947
- Volume :
- 349
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Transactions of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 9596327
- Full Text :
- https://doi.org/10.1090/S0002-9947-97-01804-7