{
  "id": "0905.4758",
  "version": "v1",
  "published": "2009-05-29T19:57:33.000Z",
  "updated": "2009-05-29T19:57:33.000Z",
  "title": "Applying the Cluster Method to Count Occurrences of Generalized Permutation Patterns",
  "authors": [
    "Andrew M. Baxter"
  ],
  "comment": "Maple package available for download: http://math.rutgers.edu/~baxter/ClusterGPP/index.html",
  "categories": [
    "math.CO"
  ],
  "abstract": "We apply ideas from the cluster method to q-count the permutations of a multiset according to the number of occurrences of certain generalized patterns, as defined by Babson and Steingrimsson. In particular, we consider those patterns with three letters and one internal dash, as well as permutation statistics composed of counting the number of occurrences of multisets of such patterns. Counting is done via recurrences which simplify in the case of permutations. A collection of Maple procedures implementing these recurrences accompanies the article.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-05-29T19:57:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05A15"
    ],
    "keywords": [
      "generalized permutation patterns",
      "cluster method",
      "count occurrences",
      "internal dash",
      "permutation statistics"
    ],
    "tags": [
      "research tool"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.4758B"
    }
  }
}