{
  "id": "0902.3074",
  "version": "v1",
  "published": "2009-02-18T09:02:00.000Z",
  "updated": "2009-02-18T09:02:00.000Z",
  "title": "On the distance between the expressions of a permutation",
  "authors": [
    "Marc Autord",
    "Patrick Dehornoy"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove that the combinatorial distance between any two reduced expressions of a given permutation of {1, ..., n} in terms of transpositions lies in O(n^4), a sharp bound. Using a connection with the intersection numbers of certain curves in van Kampen diagrams, we prove that this bound is sharp, and give a practical criterion for proving that the derivations provided by the reversing algorithm of [Dehornoy, JPAA 116 (1997) 115-197] are optimal. We also show the existence of length l expressions whose reversing requires C l^4 elementary steps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-02-18T09:02:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20B30",
      "05E15",
      "20F55",
      "20F36"
    ],
    "keywords": [
      "permutation",
      "van kampen diagrams",
      "sharp bound",
      "elementary steps",
      "intersection numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.3074A"
    }
  }
}