{
  "id": "math/0403262",
  "version": "v2",
  "published": "2004-03-16T13:56:22.000Z",
  "updated": "2004-03-24T13:07:49.000Z",
  "title": "The Number of Convex Polyominoes and the Generating Function of Jacobi Polynomials",
  "authors": [
    "Victor J. W. Guo",
    "Jiang Zeng"
  ],
  "comment": "8 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Lin and Chang gave a generating function of convex polyominoes with an $m+1$ by $n+1$ minimal bounding rectangle. Gessel showed that their result implies that the number of such polyominoes is $$ \\frac{m+n+mn}{m+n}{2m+2n\\choose 2m}-\\frac{2mn}{m+n}{m+n\\choose m}^2. $$ We show that this result can be derived from some binomial coefficients identities related to the generating function of Jacobi polynomials.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-03-24T13:07:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05A19"
    ],
    "keywords": [
      "generating function",
      "convex polyominoes",
      "jacobi polynomials",
      "binomial coefficients identities",
      "chang gave"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......3262G"
    }
  }
}