{
  "id": "0909.0103",
  "version": "v2",
  "published": "2009-09-01T06:31:30.000Z",
  "updated": "2010-03-02T19:46:20.000Z",
  "title": "The expected number of inversions after n adjacent transpositions",
  "authors": [
    "Mireille Bousquet-Mélou"
  ],
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "We give a new expression for the expected number of inversions in the product of n random adjacent transpositions in the symmetric group S_{m+1}. We then derive from this expression the asymptotic behaviour of this number when n scales with m in various ways. Our starting point is an equivalence, due to Eriksson et al., with a problem of weighted walks confined to a triangular area of the plane.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-03-02T19:46:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05A15",
      "05A16",
      "60J10"
    ],
    "keywords": [
      "expected number",
      "inversions",
      "random adjacent transpositions",
      "triangular area",
      "symmetric group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.0103B"
    }
  }
}