{
  "id": "2101.01928",
  "version": "v1",
  "published": "2021-01-06T08:53:09.000Z",
  "updated": "2021-01-06T08:53:09.000Z",
  "title": "Transformation à la Foata for special kinds of descents and excedances",
  "authors": [
    "Jean-Luc Baril",
    "Sergey Kirgizov"
  ],
  "comment": "12 pages, 2 figures",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "A pure excedance in a permutation $\\pi=\\pi_1\\pi_2\\ldots \\pi_n$ is a position $i<\\pi_i$, $1\\leq i\\leq n-1$, so that there is no $j<i$ such that $i\\leq \\pi_j<\\pi_i$. We present a one-to-one correspondence on the symmetric group that transports pure excedances to descents of special kind. As a byproduct, we prove that the popularity of pure excedances equals those of pure descents on permutations, while their distributions are different.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-06T08:53:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05A15",
      "05A19"
    ],
    "keywords": [
      "special kind",
      "transformation",
      "pure excedances equals",
      "transports pure excedances",
      "symmetric group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}