{
  "id": "2310.06288",
  "version": "v1",
  "published": "2023-10-10T03:53:29.000Z",
  "updated": "2023-10-10T03:53:29.000Z",
  "title": "Catalan-Spitzer permutations",
  "authors": [
    "Richard Ehrenborg",
    "Gábor Hetyei",
    "Margaret Readdy"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We study two classes of permutations intimately related to the visual proof of Spitzer's lemma and Huq's generalization of the Chung-Feller theorem. Both classes of permutations are counted by the Fuss-Catalan numbers. The study of one class leads to a generalization of results of Flajolet from continued fractions to continuants. The study of the other class leads to the discovery of a restricted variant of the Foata--Strehl group action.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-10T03:53:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05A05",
      "05A10",
      "05E18",
      "20B99"
    ],
    "keywords": [
      "catalan-spitzer permutations",
      "foata-strehl group action",
      "fuss-catalan numbers",
      "spitzers lemma",
      "visual proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}