{
  "id": "math/0412289",
  "version": "v1",
  "published": "2004-12-14T22:38:32.000Z",
  "updated": "2004-12-14T22:38:32.000Z",
  "title": "Some positive differences of products of Schur functions",
  "authors": [
    "Francois Bergeron",
    "Peter McNamara"
  ],
  "comment": "24 pages, 5 PostScript figures, multiple other figures use LaTeX picture environment",
  "categories": [
    "math.CO"
  ],
  "abstract": "The product $s_\\mu s_\\nu$ of two Schur functions is one of the most famous examples of a Schur-positive function, i.e. a symmetric function which, when written as a linear combination of Schur functions, has all positive coefficients. We ask when expressions of the form $s_\\lambda s_\\rho - s_\\mu s_\\nu$ are Schur-positive. This general question seems to be a difficult one, but a conjecture of Fomin, Fulton, Li and Poon says that it is the case at least when $\\lambda$ and $\\rho$ are obtained from $\\mu$ and $\\nu$ by redistributing the parts of $\\mu$ and $\\nu$ in a specific, yet natural, way. We show that their conjecture is true in several significant cases. We also formulate a skew-shape extension of their conjecture, and prove several results which serve as evidence in favor of this extension. Finally, we take a more global view by studying two classes of partially ordered sets suggested by these questions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-12-14T22:38:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "05E10"
    ],
    "keywords": [
      "schur functions",
      "positive differences",
      "conjecture",
      "general question",
      "global view"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....12289B"
    }
  }
}