{
  "id": "1305.2017",
  "version": "v1",
  "published": "2013-05-09T06:57:50.000Z",
  "updated": "2013-05-09T06:57:50.000Z",
  "title": "Four transformations on the Catalan triangle",
  "authors": [
    "Yidong Sun",
    "Fei Ma"
  ],
  "comment": "13pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we define four transformations on the classical Catalan triangle $\\mathcal{C}=(C_{n,k})_{n\\geq k\\geq 0}$ with $C_{n,k}=\\frac{k+1}{n+1}\\binom{2n-k}{n}$. The first three ones are based on the determinant and the forth is utilizing the permanent of a square matrix. It not only produces many known and new identities involving Catalan numbers, but also provides a new viewpoint on combinatorial triangles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-09T06:57:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A19",
      "05A15",
      "15A15"
    ],
    "keywords": [
      "transformations",
      "catalan numbers",
      "square matrix",
      "combinatorial triangles",
      "classical catalan triangle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.2017S"
    }
  }
}