Duality of antidiagonals and pipe dreams
Abstract
Description
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, Gröbner 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.
6 pages, 4 figures; v3=v2 = online published version: edited background exposition. (Why v3 = v2? Metadata issues.)
6 pages, 4 figures; v3=v2 = online published version: edited background exposition. (Why v3 = v2? Metadata issues.)