{
  "id": "2307.06325",
  "version": "v1",
  "published": "2023-07-12T17:44:56.000Z",
  "updated": "2023-07-12T17:44:56.000Z",
  "title": "Reversed Dickson polynomials",
  "authors": [
    "Jiaqi Fang",
    "Neranga Fernando",
    "Haoming Wu"
  ],
  "comment": "40 pages",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "We investigate fixed points and cycle types of permutation polynomials and complete permutation polynomials arising from reversed Dickson polynomials of the first kind and second kind over $\\mathbb{F}_p$. We also study the permutation behaviour of reversed Dickson polynomials of the first kind and second kind over $\\mathbb{Z}_m$. Moreover, we prove two special cases of a conjecture on the permutation behaviour of reversed Dickson polynomials over $\\mathbb{F}_p$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-12T17:44:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11T06",
      "11T55"
    ],
    "keywords": [
      "reversed dickson polynomials",
      "first kind",
      "permutation behaviour",
      "second kind",
      "complete permutation polynomials arising"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}