#### Filter Results:

#### Publication Year

1995

2002

#### Co-author

#### Key Phrase

#### Publication Venue

Learn More

This is a combinatorial study of the Poincar e polynomials of iso-typic components of a natural family of graded GL(n)-modules supported in the closure of a nilpotent conjugacy class. These polynomials generalize the Kostka-Foulkes polynomials and are q-analogues of Littlewood-Richardson coeecients. The coeecients of two-column Macdonald-Kostka polynomials… (More)

We present a simple proof of the Littlewood-Richardson rule using a sign-reversing involution, and show that a similar involution provides a com-binatorial proof of the SXP algorithm of Chen, Garsia, and Remmel 2] which computes the Schur function expansion of the plethysm of a Schur function and a power sum symmetric function. The methods of this paper… (More)

We describe the domino Schensted algorithm of Barbasch, Vogan, Garfinkle and van Leeuwen. We place this algorithm in the context of Haiman's mixed and left-right insertion algorithms and extend it to colored words. It follows easily from this description that total color of a colored word maps to the sum of the spins of a pair of 2-ribbon tableaux. Various… (More)

A graded poset structure is deened for the sets of Littlewood-Richardson (LR) tableaux that count the multiplicity of an irreducible gl(n)-module in the tensor product of irreducible gl(n)-modules corresponding to rectangular partitions. This poset generalizes the cyclage poset on column-strict tableaux deened by Lascoux and Sch utzenberger, and its grading… (More)

We study balanced labellings of diagrams representing the inversions in a permutation. These are known to be natural encodings of reduced decompositions of permutations w 2 n , and we show that they also give combinatorial descriptions of both the Stanley symmetric functions F w and and the Schubert polynomial S w associated with w. Furthermore, they lead… (More)

- ‹
- 1
- ›