{
  "id": "2203.10826",
  "version": "v1",
  "published": "2022-03-21T09:27:36.000Z",
  "updated": "2022-03-21T09:27:36.000Z",
  "title": "Joint Probabilities within Random Permutations",
  "authors": [
    "Steven Finch"
  ],
  "comment": "22 pages, 7 figures",
  "categories": [
    "math.CO",
    "cs.DM",
    "math.NT"
  ],
  "abstract": "A celebrated analogy between prime factorizations of integers and cycle decompositions of permutations is explored here. Asymptotic formulas characterizing semismooth numbers (possessing at most several large factors) carry over to random permutations. We offer a survey of practical methods for computing relevant probabilities of a bivariate or trivariate flavor.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-21T09:27:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A16",
      "05A05",
      "05A15",
      "11B37",
      "11B75",
      "92D25",
      "68Q87",
      "11Y60"
    ],
    "keywords": [
      "random permutations",
      "joint probabilities",
      "asymptotic formulas characterizing semismooth numbers",
      "prime factorizations",
      "cycle decompositions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}