{
  "id": "math/0604289",
  "version": "v2",
  "published": "2006-04-12T17:48:17.000Z",
  "updated": "2006-10-26T13:47:17.000Z",
  "title": "A Periodicity Theorem for the Octahedron Recurrence",
  "authors": [
    "Andre Henriques"
  ],
  "comment": "22 pages, (a few pictures added, section 3 has been reorganized)",
  "categories": [
    "math.CO"
  ],
  "abstract": "We investigate a variant of the octahedron recurrence which lives in a 3-dimensional lattice contained in [0,n] x [0,m] x R. Generalizing results of David Speyer math.CO/0402452, we give an explicit non-recursive formula for the values of this recurrence in terms of perfect matchings. We then use it to prove that the octahedron recurrence is periodic of period n+m. This result is reminiscent of Fomin and Zelevinsky's theorem about the periodicity of Y-systems.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-10-26T13:47:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A99"
    ],
    "keywords": [
      "octahedron recurrence",
      "periodicity theorem",
      "david speyer math",
      "explicit non-recursive formula",
      "perfect matchings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......4289H"
    }
  }
}