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arXiv:1405.2603 [math.CO]AbstractReferencesReviewsResources

A combinatorial proof that Schubert vs. Schur coefficients are nonnegative

Sami Assaf, Nantel Bergeron, Frank Sottile

Published 2014-05-11Version 1

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.

Comments: 26 pages, several colored figures
Categories: math.CO
Subjects: 05E05, 14M15
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