{
  "id": "1608.01521",
  "version": "v1",
  "published": "2016-08-04T12:56:23.000Z",
  "updated": "2016-08-04T12:56:23.000Z",
  "title": "The sandpile model on K_{m,n} and the rank of its configurations",
  "authors": [
    "Michele D'Adderio",
    "Yvan Le Borgne"
  ],
  "comment": "43 pages, 24 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We present an algorithm to compute the rank of a configuration of the sandpile model for the complete bipartite graph K_{m,n} of complexity O(m+n). Furthermore, we provide a formula for the generating function of parking sorted configurations on complete bipartite graphs K_{m,n} according to rank, degree, and the sizes m and n. The results in the present paper are similar to those found by Robert Cori and the second named author for the complete graph K_{n+1}, and they rely on the analysis of certain operators on the stable sorted configurations of K_{m,n} developed in a previous work by the authors together with Jean-Christophe Aval and Mark Dukes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-04T12:56:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sandpile model",
      "complete bipartite graph",
      "sorted configurations",
      "robert cori",
      "second named author"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}