{
  "id": "2312.01182",
  "version": "v1",
  "published": "2023-12-02T17:07:49.000Z",
  "updated": "2023-12-02T17:07:49.000Z",
  "title": "Thresholds for patterns in random permutations",
  "authors": [
    "David Bevan",
    "Dan Threlfall"
  ],
  "comment": "23 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We explore how the asymptotic structure of a random permutation of $[n]$ with $m$ inversions evolves, as $m$ increases, establishing thresholds for the appearance and disappearance of any classical, consecutive or vincular pattern. The threshold for the appearance of a classical pattern depends on the greatest number of inversions in any of its sum indecomposable components.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-02T17:07:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "60C05"
    ],
    "keywords": [
      "random permutation",
      "asymptotic structure",
      "inversions evolves",
      "greatest number",
      "sum indecomposable components"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}