2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/161520Weighted 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.)Combinatorics05E99 (Primary), 05E05, 20B30 (Secondary)text