{
  "id": "1412.4837",
  "version": "v1",
  "published": "2014-12-15T23:37:39.000Z",
  "updated": "2014-12-15T23:37:39.000Z",
  "title": "Abelian sandpile model and Biggs-Merino polynomial for directed graphs",
  "authors": [
    "Swee Hong Chan"
  ],
  "comment": "28 pages+ Appendix, 5 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "This paper is motivated by the result of Merino L{\\'o}pez that for an undirected graph G and a specified sink s, the Biggs-Merino polynomial, which is defined as a generating function of recurrent configurations of abelian sandpile model with sink, is equal to the Tutte polynomial of G. Perrot and Pham extended the definition of Biggs-Merino polynomial to directed graphs and conjectured that this polynomial is independent of the choice of sink. In this paper, we give a proof of the conjecture of Perrot and Pham, and answer the conjecture with an affirmative answer. We also observe that the Biggs-Merino polynomial is equal to the greedoid Tutte polynomial when G is an Eulerian digraph, generalizing Merino's Theorem to the setting of Eulerian digraphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-15T23:37:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C30",
      "05C31"
    ],
    "keywords": [
      "abelian sandpile model",
      "biggs-merino polynomial",
      "directed graphs",
      "eulerian digraph",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.4837C"
    }
  }
}