{
  "id": "1405.6802",
  "version": "v1",
  "published": "2014-05-27T06:15:16.000Z",
  "updated": "2014-05-27T06:15:16.000Z",
  "title": "On the growth rate of 1324-avoiding permutations",
  "authors": [
    "Andrew R Conway",
    "Anthony J Guttmann"
  ],
  "comment": "20 pages, 10 figures",
  "categories": [
    "math.CO",
    "cs.DS",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We give an improved algorithm for counting the number of $1324$-avoiding permutations, resulting in 5 further terms of the generating function. We analyse the known coefficients and find compelling evidence that unlike other classical length-4 pattern-avoiding permutations, the generating function in this case does not have an algebraic singularity. Rather, the number of 1324-avoiding permutations of length $n$ behaves as $$B\\cdot \\mu^n \\cdot \\mu_1^{n^{\\sigma}} \\cdot n^g.$$ We estimate $\\mu=11.60 \\pm 0.01,$ $\\sigma=1/2,$ $\\mu_1 = 0.0398 \\pm 0.0010,$ $g = -1.1 \\pm 0.2$ and $B =9.5 \\pm 1.0.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-27T06:15:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05A15",
      "05A16"
    ],
    "keywords": [
      "growth rate",
      "generating function",
      "algebraic singularity",
      "compelling evidence",
      "pattern-avoiding permutations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.6802C"
    }
  }
}