{
  "id": "1412.1184",
  "version": "v1",
  "published": "2014-12-03T04:35:03.000Z",
  "updated": "2014-12-03T04:35:03.000Z",
  "title": "$G$-strongly positive scripts and critical configurations of chip firing games on digraphs",
  "authors": [
    "Tran Thi Thu Huong"
  ],
  "comment": "13 pages, 2 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We show a collection of scripts, called $G$-strongly positive scripts, which is used to recognize critical configurations of a chip firing game (CFG) on a multi-digraph with a global sink. To decrease the time of the process of recognition caused by the stabilization we present an algorithm to find the minimum G-strongly positive script. From that we prove the non-stability of configurations obtained from a critical configuration by firing inversely any non-empty multi-subset of vertices. This result is a generalization of a very recent one by Aval \\emph{et.al} which is applied for CFG on undirected graphs. Last, we give a combinatorial proof for the duality between critical and super-stable configurations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-03T04:35:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "chip firing game",
      "strongly positive scripts",
      "minimum g-strongly positive script",
      "global sink",
      "non-empty multi-subset"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.1184T"
    }
  }
}