{
  "id": "2403.17110",
  "version": "v1",
  "published": "2024-03-25T18:47:48.000Z",
  "updated": "2024-03-25T18:47:48.000Z",
  "title": "Fixed points and cycles of parking functions",
  "authors": [
    "Martin Rubey",
    "Mei Yin"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A parking function of length $n$ is a sequence $\\pi=(\\pi_1,\\dots, \\pi_n)$ of positive integers such that if $\\lambda_1\\leq\\cdots\\leq \\lambda_n$ is the increasing rearrangement of $\\pi_1,\\dots,\\pi_n$, then $\\lambda_i\\leq i$ for $1\\leq i\\leq n$. In this paper we obtain some exact results on the number of fixed points and cycles of parking functions. Our proofs will be based on generalizations of Pollak's argument. Extensions of our techniques are discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-25T18:47:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05A19",
      "60C05"
    ],
    "keywords": [
      "parking function",
      "fixed points",
      "exact results",
      "pollaks argument",
      "positive integers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}