{
  "id": "1310.2930",
  "version": "v1",
  "published": "2013-10-10T19:45:47.000Z",
  "updated": "2013-10-10T19:45:47.000Z",
  "title": "Schur-positivity in a Square",
  "authors": [
    "Cristina Ballantine",
    "Rosa Orellana"
  ],
  "comment": "28 pages, 16 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Determining if a symmetric function is Schur-positive is a prevalent and, in general, a notoriously difficult problem. In this paper we study the Schur-positivity of a family of symmetric functions. Given a partition \\lambda, we denote by \\lambda^c its complement in a square partition (m^m). We conjecture a Schur-positivity criterion for symmetric functions of the form s_{\\mu'}s_{\\mu^c}-s_{\\lambda'}s_{\\lambda^c}, where \\lambda is a partition of weight |\\mu|-1 contained in \\mu and the complement of \\mu is taken in the same square partition as the complement of \\lambda. We prove the conjecture in many cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-10T19:45:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E10",
      "05E05",
      "20C30"
    ],
    "keywords": [
      "symmetric function",
      "square partition",
      "complement",
      "conjecture",
      "schur-positivity criterion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.2930B"
    }
  }
}