{
  "id": "math/0606170",
  "version": "v1",
  "published": "2006-06-08T19:56:39.000Z",
  "updated": "2006-06-08T19:56:39.000Z",
  "title": "Meanders in a Cayley graph",
  "authors": [
    "H. Tracy Hall"
  ],
  "categories": [
    "math.CO",
    "math.GR",
    "math.GT"
  ],
  "abstract": "A meander of order n is a simple closed curve in the plane which intersects a horizontal line transversely at 2n points. (Meanders which differ by an isotopy of the line and plane are considered equivalent.) Let Gamma_n be the Cayley graph of the symmetric group S_n as generated by all (n choose 2) transpositions. Let Lambda_n be any interval of maximal length in Gamma_n; this graph is the Hasse diagram of the lattice of noncrossing partitions. The meanders of order n are in one-to-one correspondence with ordered pairs of maximally separated vertices of Lambda_n.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-06-08T19:56:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M20"
    ],
    "keywords": [
      "cayley graph",
      "one-to-one correspondence",
      "simple closed curve",
      "hasse diagram",
      "maximal length"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......6170H"
    }
  }
}