{
  "id": "math/0503204",
  "version": "v1",
  "published": "2005-03-10T19:48:32.000Z",
  "updated": "2005-03-10T19:48:32.000Z",
  "title": "Symmetric Groups and Expanders",
  "authors": [
    "Martin Kassabov"
  ],
  "comment": "10 pages",
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "We construct an explicit generating sets $F_n$ and $\\tilde F_n$ of the alternating and the symmetric groups, which make the Cayley graphs $C(Alt(n), F_n)$ and $C(Sym(n), \\tilde F_n)$ a family of bounded degree expanders for all sufficiently large $n$. These expanders have many applications in the theory of random walks on groups and other areas of mathematics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-03-10T19:48:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20B30",
      "05C25",
      "05E15",
      "20C30",
      "20F69",
      "60C05",
      "68R05",
      "68R10"
    ],
    "keywords": [
      "symmetric groups",
      "explicit generating sets",
      "cayley graphs",
      "bounded degree expanders",
      "random walks"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......3204K"
    }
  }
}