{
  "id": "0711.2223",
  "version": "v1",
  "published": "2007-11-14T15:33:57.000Z",
  "updated": "2007-11-14T15:33:57.000Z",
  "title": "Pattern avoidance and the Bruhat order on involutions",
  "authors": [
    "Axel Hultman",
    "Kathrin Vorwerk"
  ],
  "comment": "14 pages, 5 figures",
  "journal": "J. Algebraic Combin. 30 (2009), no. 1, 87--102",
  "categories": [
    "math.CO"
  ],
  "abstract": "We show that the principal order ideal below an element w in the Bruhat order on involutions in a symmetric group is a Boolean lattice if and only if w avoids the patterns 4321, 45312 and 456123. Similar criteria for signed permutations are also stated. Involutions with this property are enumerated with respect to natural statistics. In this context, a bijective correspondence with certain Motzkin paths is demonstrated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-11-14T15:33:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bruhat order",
      "pattern avoidance",
      "involutions",
      "principal order ideal",
      "symmetric group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.2223H"
    }
  }
}