2014/05/11 by Sami Assaf, Nantel Bergeron, Assaf, Sami +3
Mathematics · #05E05 #14M15 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1405.2603
openalex publication_date 2014/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.