{
  "id": "math/0703868",
  "version": "v2",
  "published": "2007-03-29T07:09:27.000Z",
  "updated": "2008-07-24T17:01:11.000Z",
  "title": "The Sandpile Group of a Tree",
  "authors": [
    "Lionel Levine"
  ],
  "comment": "v2 incorporates referee comments, corrects references, improves notation",
  "journal": "European Journal of Combinatorics 30(4): 1026--1035, 2009",
  "doi": "10.1016/j.ejc.2008.02.014",
  "categories": [
    "math.CO"
  ],
  "abstract": "A wired tree is a graph obtained from a tree by collapsing the leaves to a single vertex. We describe a pair of short exact sequences relating the sandpile group of a wired tree to the sandpile groups of its principal subtrees. In the case of a regular tree these sequences split, enabling us to compute the full decomposition of the sandpile group as a product of cyclic groups. This resolves in the affirmative a conjecture of E. Toumpakari concerning the ranks of the Sylow p-subgroups.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-07-24T17:01:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C25",
      "05C05"
    ],
    "keywords": [
      "sandpile group",
      "wired tree",
      "cyclic groups",
      "full decomposition",
      "single vertex"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......3868L"
    }
  }
}