{
  "id": "math/0604322",
  "version": "v1",
  "published": "2006-04-13T17:14:36.000Z",
  "updated": "2006-04-13T17:14:36.000Z",
  "title": "Pattern Avoidance and the Bruhat Order",
  "authors": [
    "Bridget Eileen Tenner"
  ],
  "comment": "18 pages, 7 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The structure of order ideals in the Bruhat order for the symmetric group is elucidated via permutation patterns. A method for determining non-isomorphic principal order ideals is described and applied for small lengths. The permutations with boolean principal order ideals are characterized. These form an order ideal which is a simplicial poset, and its rank generating function is computed. Moreover, the permutations whose principal order ideals have a form related to boolean posets are also completely described. It is determined when the set of permutations avoiding a particular set of patterns is an order ideal, and the rank generating functions of these ideals are computed. Finally, the Bruhat order in types B and D is studied, and the elements with boolean principal order ideals are characterized and enumerated by length.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-04-13T17:14:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E15",
      "06A07",
      "05A05"
    ],
    "keywords": [
      "bruhat order",
      "boolean principal order ideals",
      "pattern avoidance",
      "rank generating function",
      "permutation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......4322T"
    }
  }
}