A combinatorial proof that Schubert vs. Schur coefficients are nonnegative
Combinatorics
2014-05-13 v1
Abstract
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.
Cite
@article{arxiv.1405.2603,
title = {A combinatorial proof that Schubert vs. Schur coefficients are nonnegative},
author = {Sami Assaf and Nantel Bergeron and Frank Sottile},
journal= {arXiv preprint arXiv:1405.2603},
year = {2014}
}
Comments
26 pages, several colored figures