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arXiv · 0706.3031

Duality of antidiagonals and pipe dreams

Ning Jia·Ezra Miller
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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.

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Ning Jia, Ezra Miller. 2008-05-26. Duality of antidiagonals and pipe dreams. https://arxiv.org/abs/0706.3031

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