{
  "id": "1901.08506",
  "version": "v1",
  "published": "2019-01-24T17:03:07.000Z",
  "updated": "2019-01-24T17:03:07.000Z",
  "title": "Most principal permutation classes have nonrational generating functions",
  "authors": [
    "Miklós Bóna"
  ],
  "comment": "10 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We prove that for any fixed $n$, and for most permutation patterns $q$, the number $Av_{n,\\ell}(q)$ of $q$-avoiding permutations of length $n$ that consist of $\\ell$ skew blocks is a monotone decreasing function of $\\ell$. We then show that this implies that for most patterns $q$, the generating function $\\sum_{n\\geq 0} Av_n(q)z^n$ of the sequence $Av_n(q)$ of the numbers of $q$-avoiding permutations is not rational.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-24T17:03:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05A15",
      "05A16",
      "05A19",
      "05A20"
    ],
    "keywords": [
      "principal permutation classes",
      "nonrational generating functions",
      "avoiding permutations",
      "monotone decreasing function",
      "permutation patterns"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}