{
  "id": "1004.2685",
  "version": "v2",
  "published": "2010-04-15T18:35:01.000Z",
  "updated": "2011-01-03T21:08:14.000Z",
  "title": "A quasisymmetric function generalization of the chromatic symmetric function",
  "authors": [
    "Brandon Humpert"
  ],
  "comment": "14 pages, 5 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The chromatic symmetric function $X_G$ of a graph $G$ was introduced by Stanley. In this paper we introduce a quasisymmetric generalization $X^k_G$ called the $k$-chromatic quasisymmetric function of $G$ and show that it is positive in the fundamental basis for the quasisymmetric functions. Following the specialization of $X_G$ to $\\chi_G(\\lambda)$, the chromatic polynomial, we also define a generalization $\\chi^k_G(\\lambda)$ and show that evaluations of this polynomial for negative values generalize a theorem of Stanley relating acyclic orientations to the chromatic polynomial.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-01-03T21:08:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "chromatic symmetric function",
      "quasisymmetric function generalization",
      "chromatic polynomial",
      "chromatic quasisymmetric function",
      "stanley relating acyclic orientations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.2685H"
    }
  }
}