{
  "id": "1311.7228",
  "version": "v2",
  "published": "2013-11-28T07:28:45.000Z",
  "updated": "2013-12-16T19:31:42.000Z",
  "title": "A curious polynomial interpolation of Carlitz-Riordan's $q$-ballot numbers",
  "authors": [
    "Frédéric Chapoton",
    "Jiang Zeng"
  ],
  "comment": "15 pages, some connections with J. Cigler's earlier work is mentioned",
  "categories": [
    "math.CO"
  ],
  "abstract": "We study a polynomial sequence $C_n(x|q)$ defined as a solution of a $q$-difference equation. This sequence, evaluated at $q$-integers, interpolates Carlitz-Riordan's $q$-ballot numbers. In the basis given by some kind of $q$-binomial coefficients, the coefficients are again some $q$-ballot numbers. We obtain in a combinatorial way another curious recurrence relation for these polynomials.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-12-16T19:31:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ballot numbers",
      "curious polynomial interpolation",
      "difference equation",
      "interpolates carlitz-riordans",
      "binomial coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.7228C"
    }
  }
}