{
  "id": "1205.1596",
  "version": "v1",
  "published": "2012-05-08T06:11:11.000Z",
  "updated": "2012-05-08T06:11:11.000Z",
  "title": "Bounds on the diameter of Cayley graphs of the symmetric group",
  "authors": [
    "John Bamberg",
    "Nick Gill",
    "Thomas Hayes",
    "Harald Helfgott",
    "Ákos Seress",
    "Pablo Spiga"
  ],
  "comment": "17 pages, 6 tables",
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "In this paper we are concerned with the conjecture that, for any set of generators S of the symmetric group of degree n, the word length in terms of S of every permutation is bounded above by a polynomial of n. We prove this conjecture for sets of generators containing a permutation fixing at least 37% of the points.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-08T06:11:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetric group",
      "cayley graphs",
      "permutation",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.1596B"
    }
  }
}