{
  "id": "1902.02240",
  "version": "v1",
  "published": "2019-02-06T15:42:53.000Z",
  "updated": "2019-02-06T15:42:53.000Z",
  "title": "Chromatic Polynomial and Heaps of Pieces",
  "authors": [
    "Bishal Deb"
  ],
  "comment": "16 pages, 4 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Stanley in his paper [Stanley, Richard P.: Acyclic orientations of graphs In: Discrete Mathematics 5 (1973), Nr. 2, S. 171-178.] provided interpretations of the chromatic polynomial when it is substituted with negative integers. Greene and Zaslavsky interpreted the coefficients of the chromatic polynomial in [Greene, Curtis ; Zaslavsky, Thomas: On the interpretation of Whitney numbers through arrangements of hyperplanes, zonotopes, non-Radon partitions, and orientations of graphs. In: Transactions of the American Mathematical Society 280 (1983), jan, Nr. 1, S. 97-97.]. We shall develop an involution on factorisations of heaps of pieces and using this involution, we shall provide bijective proofs to results from both the papers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-06T15:42:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "chromatic polynomial",
      "acyclic orientations",
      "involution",
      "interpretation",
      "whitney numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}