{
  "id": "math/0604471",
  "version": "v1",
  "published": "2006-04-21T19:14:39.000Z",
  "updated": "2006-04-21T19:14:39.000Z",
  "title": "A Combinatorial Interpretation of j/n {kn}\\choose{n+j}",
  "authors": [
    "David Callan"
  ],
  "comment": "Latex, 7 pages, 5 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The identity j/n {kn}\\choose{n+j} =(k-1) {kn-1}\\choose{n+j-1}- {kn-1}\\choose{n+j} shows that j/n {kn}\\choose{n+j} is always an integer. Here we give a combinatorial interpretation of this integer in terms of lattice paths, using a uniformly distributed statistic. In particular, the case j=1,k=2 gives yet another manifestation of the Catalan numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-04-21T19:14:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15"
    ],
    "keywords": [
      "combinatorial interpretation",
      "catalan numbers",
      "identity j/n",
      "lattice paths"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......4471C"
    }
  }
}