{
  "id": "1904.01262",
  "version": "v1",
  "published": "2019-04-02T07:49:38.000Z",
  "updated": "2019-04-02T07:49:38.000Z",
  "title": "Combinatorial reciprocity for the chromatic polynomial and the chromatic symmetric function",
  "authors": [
    "Olivier Bernardi",
    "Philippe Nadeau"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let G be a graph, and let $\\chi$G be its chromatic polynomial. For any non-negative integers i, j, we give an interpretation for the evaluation $\\chi$ (i) G (--j) in terms of acyclic orientations. This recovers the classical interpretations due to Stanley and to Green and Zaslavsky respectively in the cases i = 0 and j = 0. We also give symmetric function refinements of our interpretations, and some extensions. The proofs use heap theory in the spirit of a 1999 paper of Gessel.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-02T07:49:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "chromatic symmetric function",
      "chromatic polynomial",
      "combinatorial reciprocity",
      "symmetric function refinements",
      "acyclic orientations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}