{
  "id": "math/0507038",
  "version": "v2",
  "published": "2005-07-03T02:04:52.000Z",
  "updated": "2007-07-05T23:46:39.000Z",
  "title": "Set maps, umbral calculus, and the chromatic polynomial",
  "authors": [
    "Gus Wiseman"
  ],
  "comment": "20 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Some important properties of the chromatic polynomial also hold for any polynomial set map satisfying p_S(x+y)=\\sum_{T\\uplus U=S}p_T(x)p_U(y). Using umbral calculus, we give a formula for the expansion of such a set map in terms of any polynomial sequence of binomial type. This leads to some new expansions of the chromatic polynomial. We also describe a set map generalization of Abel polynomials.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-07-05T23:46:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05A40",
      "05A18"
    ],
    "keywords": [
      "chromatic polynomial",
      "umbral calculus",
      "set map generalization",
      "polynomial set map satisfying",
      "important properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......7038W"
    }
  }
}