{
  "id": "1903.06589",
  "version": "v1",
  "published": "2019-03-15T15:09:17.000Z",
  "updated": "2019-03-15T15:09:17.000Z",
  "title": "New combinatorial interpretation of the binomial coefficients",
  "authors": [
    "Paul M. Rakotomamonjy",
    "Sandrataniaina R. Andriantsoa"
  ],
  "comment": "12 pages, 2 figures and 1 table",
  "categories": [
    "math.CO"
  ],
  "abstract": "Using generating functions and some trivial bijections, we show in this paper that the binomial coefficients count the set of (123,132) and (123,213)-avoiding permutations according to the number of crossings. We also define a q-tableau of power of two and prove that it counts the set of (213,312) and (132,312)-avoiding permutations according to the number of crossings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-15T15:09:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A20",
      "05A05"
    ],
    "keywords": [
      "combinatorial interpretation",
      "binomial coefficients count",
      "trivial bijections",
      "permutations",
      "generating functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}