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- Ezra Miller, Bernd Sturmfels, Matthias Beck, Carlos D 'andrea, Mike Develin, Nicholas Eriksson +40 others

Preface The last decade has seen a number of exciting developments at the intersection of commutative algebra with combinatorics. New methods have evolved out of an influx of ideas from such diverse areas as polyhedral geometry, theoretical physics, representation theory, homological algebra, symplectic geometry, graph theory, integer programming, symbolic… (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 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)

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 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)

- Anders Skovsted Buch, Andrew Kresch, Mark Shimozono, Harry Tamvakis, Alexander Yong
- 2004

We give a nonrecursive combinatorial formula for the expansion of a stable Grothendieck polynomial in the basis of stable Grothendieck poly-nomials for partitions. The proof is based on a generalization of the Edelman-Greene insertion algorithm. This result is applied to prove a number of formulas and properties for K-theoretic quiver polynomials and… (More)