{
  "id": "1212.2530",
  "version": "v2",
  "published": "2012-12-11T16:42:44.000Z",
  "updated": "2013-03-24T16:11:59.000Z",
  "title": "Pattern Avoidance in Ordered Set Partitions",
  "authors": [
    "Anant Godbole",
    "Adam Goyt",
    "Jennifer Herdan",
    "Lara Pudwell"
  ],
  "comment": "19 pages, 2 figures; Now includes a proof of what was Conjecture 1, and a generalization thereof",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper we consider the enumeration of ordered set partitions avoiding a permutation pattern of length 2 or 3. We provide an exact enumeration for avoiding the permutation 12. We also give exact enumeration for ordered partitions with 3 blocks and ordered partitions with n-1 blocks avoiding a permutation of length 3. We use enumeration schemes to recursively enumerate 123-avoiding ordered partitions with any block sizes. Finally, we give some asymptotic results for the growth rates of the number of ordered set partitions avoiding a single pattern; including a Stanley-Wilf type that exhibits existence of such growth rates.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-03-24T16:11:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A18",
      "05A05",
      "05A15",
      "05A16"
    ],
    "keywords": [
      "pattern avoidance",
      "ordered partitions",
      "ordered set partitions avoiding",
      "growth rates",
      "exact enumeration"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.2530G"
    }
  }
}