{
  "id": "1109.6393",
  "version": "v2",
  "published": "2011-09-29T03:46:52.000Z",
  "updated": "2012-10-02T05:03:58.000Z",
  "title": "Counting the spanning trees of the 3-cube using edge slides",
  "authors": [
    "Christopher Tuffley"
  ],
  "comment": "17 pages, 9 figures. v2: Final version as published in the Australasian Journal of Combinatorics. Section 5 shortened and restructured; references added; one figure added; some typos corrected; additional minor changes in response to the referees' comments",
  "journal": "Australas. J. Combin., 54:189-206, 2012",
  "categories": [
    "math.CO"
  ],
  "abstract": "We give a direct combinatorial proof of the known fact that the 3-cube has 384 spanning trees, using an \"edge slide\" operation on spanning trees. This gives an answer in the case n=3 to a question implicitly raised by Stanley. Our argument also gives a bijective proof of the n=3 case of a weighted count of the spanning trees of the n-cube due to Martin and Reiner.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-10-02T05:03:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C30",
      "05C05"
    ],
    "keywords": [
      "spanning trees",
      "edge slide",
      "direct combinatorial proof",
      "bijective proof",
      "weighted count"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.6393T"
    }
  }
}