Séminaire Lotharingien de Combinatoire, B58e (2008), 6 pp.

Ning Jia and Ezra Miller

Duality of Antidiagonals and Pipe Dreams

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, 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.

Received: July 5, 2007. Accepted: May 17, 2008. Final Version: May 18, 2008.

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