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A combinatorial proof that Schubert vs. Schur coefficients are nonnegative

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arxiv 1405.2603 v1 pith:6XQG5JM4 submitted 2014-05-11 math.CO

Sami Assaf , Nantel Bergeron , Frank Sottile This is my paper · ORCID
classification math.CO
keywords proofschubertcombinatorialnonnegativepolynomialschurassafbergeron
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We give a combinatorial proof that the product of a Schubert polynomial by a Schur polynomial is a nonnegative sum of Schubert polynomials. Our proof uses Assaf's theory of dual equivalence to show that a quasisymmetric function of Bergeron and Sottile is Schur-positive. By a geometric comparison theorem of Buch and Mihalcea, this implies the nonnegativity of Gromov-Witten invariants of the Grassmannian.

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  1. A Littlewood-Richardson Rule for Forest Polynomials via the Schubert Bialgebra

    math.CO 2026-06 unverdicted novelty 7.0 of 10

    A Littlewood-Richardson rule counts pairs of forest RC graphs whose lift product matches a target forest-code and weight c, and the same rule applies to dual bases via a new Schubert bialgebra.

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