Mathematics – Combinatorics
Scientific paper
2005-02-16
Mathematics
Combinatorics
36 pages
Scientific paper
We study a family of polynomials whose values express degrees of Schubert varieties in the generalized complex flag manifold G/B. The polynomials are given by weighted sums over saturated chains in the Bruhat order. We derive several explicit formulas for these polynomials, and investigate their relations with Schubert polynomials, harmonic polynomials, Demazure characters, and generalized Littlewood-Richardson coefficients. In the second half of the paper, we concern with the case of to the classical flag manifold of Lie type A and discuss related combinatorial objects: flagged Schur polynomials, 312-avoiding permutations, generalized Gelfand-Tsetlin polytopes, the inverse Schubert-Kostka matrix, parking functions, and binary trees.
Postnikov Alexander
Stanley Richard P.
No associations
LandOfFree
Chains in the Bruhat order does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Chains in the Bruhat order, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Chains in the Bruhat order will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-97414