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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