{
  "id": "1404.3395",
  "version": "v3",
  "published": "2014-04-13T15:53:20.000Z",
  "updated": "2014-06-23T10:34:09.000Z",
  "title": "Nested sets, set partitions and Kirkman-Cayley dissection numbers",
  "authors": [
    "Giovanni Gaiffi"
  ],
  "comment": "With respect to v1: minor changes in the notation and correction of some misprints With respect to v2: added references",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper we show a a proof by explicit bijections of the famous Kirkman-Cayley formula for the number of dissections of a convex polygon. Our starting point is the bijective correspondence between the set of nested sets made by \\(k\\) subsets of \\(\\{1,2,...,n\\}\\) with cardinality \\(\\geq 2\\) and the set of partitions of \\(\\{1,2,...,n+k-1\\}\\) into \\(k\\) parts with cardinality \\(\\geq 2\\).",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-06-23T10:34:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A19"
    ],
    "keywords": [
      "kirkman-cayley dissection numbers",
      "nested sets",
      "set partitions",
      "famous kirkman-cayley formula",
      "explicit bijections"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.3395G"
    }
  }
}