{
  "id": "1209.2404",
  "version": "v1",
  "published": "2012-09-11T19:32:47.000Z",
  "updated": "2012-09-11T19:32:47.000Z",
  "title": "On the Best Upper Bound for Permutations Avoiding A Pattern of a Given Length",
  "authors": [
    "Miklos Bona"
  ],
  "comment": "12 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Numerical evidence suggests that certain permutation patterns of length k are easier to avoid than any other patterns of that same length. We prove that these patterns are avoided by no more than (2.25k^2)^n permutations of length n. In light of this, we conjecture that no pattern of length k is avoided by more than that many permutations of length n.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-09-11T19:32:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05A16"
    ],
    "keywords": [
      "best upper bound",
      "permutations avoiding",
      "permutation patterns",
      "numerical evidence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.2404B"
    }
  }
}