{
  "id": "0910.1343",
  "version": "v1",
  "published": "2009-10-07T19:53:26.000Z",
  "updated": "2009-10-07T19:53:26.000Z",
  "title": "The absence of a pattern and the number of occurrences of another",
  "authors": [
    "Miklos Bona"
  ],
  "comment": "16 pages, 3 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Following a question of J. Cooper, we study the expected number of occurrences of a given permutation pattern $q$ in permutations that avoid another given pattern $r$. In some cases, we find the pattern that occurs least often, (resp. most often) in all $r$-avoiding permutations. We also prove a few exact enumeration formulae, some of which are surprising.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-10-07T19:53:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05A16"
    ],
    "keywords": [
      "occurrences",
      "exact enumeration formulae",
      "avoiding permutations",
      "expected number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.1343B"
    }
  }
}