{
  "id": "1206.0320",
  "version": "v2",
  "published": "2012-06-01T22:19:37.000Z",
  "updated": "2012-07-12T15:20:47.000Z",
  "title": "Expected Patterns in Permutation Classes",
  "authors": [
    "Cheyne Homberger"
  ],
  "journal": "Electronic Journal of Combinatorics, 19(3) (2012), P43",
  "categories": [
    "math.CO"
  ],
  "abstract": "In the set of all patterns in $S_n$, it is clear that each k-pattern occurs equally often. If we instead restrict to the class of permutations avoiding a specific pattern, the situation quickly becomes more interesting. Mikl\\'os B\\'ona recently proved that, surprisingly, if we consider the class of permutations avoiding the pattern 132, all other non-monotone patterns of length 3 are equally common. In this paper we examine the class $\\Av (123)$, and give exact formula for the occurrences of each length 3 pattern. While this class does not break down as nicely as $\\Av (132)$, we find some interesting similarities between the two and prove that the number of 231 patterns is the same in each.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-07-12T15:20:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "permutation classes",
      "expected patterns",
      "permutations avoiding",
      "instead restrict",
      "miklos bona"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.0320H"
    }
  }
}