{
  "id": "2104.12019",
  "version": "v1",
  "published": "2021-04-24T20:34:42.000Z",
  "updated": "2021-04-24T20:34:42.000Z",
  "title": "Cycle type of random permutations: A toolkit",
  "authors": [
    "Kevin Ford"
  ],
  "comment": "27 pages",
  "categories": [
    "math.CO",
    "math.GR",
    "math.NT",
    "math.PR"
  ],
  "abstract": "We prove a number of results, new and old, about the cycle type of a random permutation on S_n. Underlying our analysis is the idea that the number of cycles of size k is roughly Poisson distributed with parameter 1/k. In particular, we establish strong results about the distribution of the number of cycles whose lengths lie in a fixed but arbitrary set I. Our techniques are motivated by the theory of sieves in number theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-24T20:34:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random permutation",
      "cycle type",
      "number theory",
      "arbitrary set",
      "lengths lie"
    ],
    "tags": [
      "research tool"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}