{
  "id": "1405.2603",
  "version": "v1",
  "published": "2014-05-11T23:55:52.000Z",
  "updated": "2014-05-11T23:55:52.000Z",
  "title": "A combinatorial proof that Schubert vs. Schur coefficients are nonnegative",
  "authors": [
    "Sami Assaf",
    "Nantel Bergeron",
    "Frank Sottile"
  ],
  "comment": "26 pages, several colored figures",
  "categories": [
    "math.CO"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-11T23:55:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "14M15"
    ],
    "keywords": [
      "combinatorial proof",
      "schur coefficients",
      "schubert polynomial",
      "geometric comparison theorem",
      "dual equivalence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.2603A"
    }
  }
}