Duality of antidiagonals and pipe dreams
Combinatorics
2008-05-27 v3
Abstract
Weighted enumeration of reduced pipe dreams (or rc-graphs) results in a combinatorial expression for Schubert polynomials. The duality between the set of reduced pipe dreams and certain antidiagonals has important geometric implications [A. Knutson and E. Miller, Gr\"obner geometry of Schubert polynomials, Ann. Math. 161, 1245-1318]. The original proof of the duality was roundabout, relying on the algebra of certain monomial ideals and a recursive characterization of reduced pipe dreams. This paper provides a direct combinatorial proof.
Cite
@article{arxiv.0706.3031,
title = {Duality of antidiagonals and pipe dreams},
author = {Ning Jia and Ezra Miller},
journal= {arXiv preprint arXiv:0706.3031},
year = {2008}
}