{
  "id": "2007.07771",
  "version": "v1",
  "published": "2020-07-15T15:44:17.000Z",
  "updated": "2020-07-15T15:44:17.000Z",
  "title": "On the Central Description of the Group of Riordan Arrays",
  "authors": [
    "Paul Barry"
  ],
  "comment": "17 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We provide an alternative description of the group of Riordan arrays, by using two power series of the form $\\sum_{n=0}^{\\infty} g_n x^n$, where $g_0 \\ne 0$ to build a typical element of the constructed group. We relate these elements to Riordan arrays in the usual description, showing that each newly constructed element is the vertical half of a \"usual\" element. The product rules and the construction of the inverse are given in this new description, which we call a \"central\" description, because of links to the central coefficients of Riordan arrays. This is done for the case of ordinary generating functions. Finally, we briefly look at the exponential case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-15T15:44:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A30",
      "15B36",
      "11C20",
      "20G05",
      "20H25",
      "15A30",
      "15B36",
      "11C20",
      "20G05",
      "20H25"
    ],
    "keywords": [
      "riordan arrays",
      "central description",
      "power series",
      "central coefficients",
      "product rules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}