{
  "id": "0711.2684",
  "version": "v1",
  "published": "2007-11-16T21:42:31.000Z",
  "updated": "2007-11-16T21:42:31.000Z",
  "title": "Bijections from Dyck paths to 321-avoiding permutations revisited",
  "authors": [
    "David Callan"
  ],
  "comment": "15 pages, LaTeX",
  "categories": [
    "math.CO"
  ],
  "abstract": "There are (at least) three bijections from Dyck paths to 321-avoiding permutations in the literature, due to Billey-Jockusch-Stanley, Krattenthaler, and Mansour-Deng-Du. How different are they? Denoting them B,K,M respectively, we show that M = B \\circ L = K \\circ L' where L is the classical Kreweras-Lalanne involution on Dyck paths and L', also an involution, is a sort of derivative of L. Thus K^{-1} \\circ B, a measure of the difference between B and K, is the product of involutions L' \\circ L and turns out to be a very curious bijection: as a permutation on Dyck n-paths it is an nth root of the \"reverse path\" involution. The proof of this fact boils down to a geometric argument involving pairs of nonintersecting lattice paths.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-11-16T21:42:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15"
    ],
    "keywords": [
      "dyck paths",
      "permutations",
      "nth root",
      "classical kreweras-lalanne involution",
      "nonintersecting lattice paths"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.2684C"
    }
  }
}