{
  "id": "1702.04051",
  "version": "v1",
  "published": "2017-02-14T02:42:21.000Z",
  "updated": "2017-02-14T02:42:21.000Z",
  "title": "Weak dual equivalence for polynomials",
  "authors": [
    "Sami Assaf"
  ],
  "comment": "26 pages, 23 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We use dual equivalence to give a short, combinatorial proof that Stanley symmetric functions are Schur positive. We introduce weak dual equivalence, and use it to give a short, combinatorial proof that Schubert polynomials are key positive. To demonstrate further the utility of this new tool, we use weak dual equivalence to prove a nonnegative Littlewood--Richardson rule for the key expansion of the product of a key polynomial and a Schur polynomial, and to introduce skew key polynomials that, when skewed by a partition, expand nonnegatively in the key basis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-14T02:42:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "05A15",
      "05A19",
      "05E10",
      "05E18",
      "14N15"
    ],
    "keywords": [
      "weak dual equivalence",
      "combinatorial proof",
      "stanley symmetric functions",
      "schur polynomial",
      "schubert polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}