{
  "id": "1312.3164",
  "version": "v1",
  "published": "2013-12-11T13:52:10.000Z",
  "updated": "2013-12-11T13:52:10.000Z",
  "title": "A determinant representation for generalized ballot and Fuss-Catalan numbers",
  "authors": [
    "James J. Y. Zhao"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In this note we introduce a determinant and then give its evaluating formula. The determinant turns out to be a generalization of the well-known ballot and Fuss-Catalan numbers, which is believed to be new. The evaluating formula is proved by showing that the determinant coincides with the number of lattice paths with (1,0), (0,1)-steps in the plane that stay below a boundary line of rational slope.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-11T13:52:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05A10",
      "15A15",
      "15B36"
    ],
    "keywords": [
      "fuss-catalan numbers",
      "determinant representation",
      "generalized ballot",
      "evaluating formula",
      "well-known ballot"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.3164Z"
    }
  }
}