{
  "id": "2206.04021",
  "version": "v1",
  "published": "2022-06-08T17:27:18.000Z",
  "updated": "2022-06-08T17:27:18.000Z",
  "title": "Fixed points of powers of permutations",
  "authors": [
    "Melvyn B. Nathanson"
  ],
  "comment": "9 pages",
  "categories": [
    "math.CO",
    "math.GR",
    "math.NT"
  ],
  "abstract": "Let $\\sigma$ be a permutation of a finite or infinite set $X$, and let $F_X\\left( \\sigma^k\\right)$ be the number of fixed points of the $k$th power of $\\sigma$. This paper describes how the sequence $\\left(F_X\\left( \\sigma^k\\right) \\right)_{k=1}^{\\infty}$ determines the permutation $\\sigma$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-08T17:27:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20B05",
      "20B07",
      "20B10",
      "20F69"
    ],
    "keywords": [
      "fixed points",
      "permutation",
      "infinite set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}