Duality of antidiagonals and pipe dreams

Details Duality of antidiagonals and pipe dreams Duality of antidiagonals and pipe dreams

2007-06-20

arxiv.org/abs/0706.3031v3

S\'eminaire Lotharingien de Combinatoire, Issue 58 (2008), Article B58e. (electronic)

Mathematics

Combinatorics

6 pages, 4 figures; v3=v2 = online published version: edited background exposition. (Why v3 = v2? Metadata issues.)

Scientific paper

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.

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