{
  "id": "2207.02719",
  "version": "v1",
  "published": "2022-07-06T14:45:06.000Z",
  "updated": "2022-07-06T14:45:06.000Z",
  "title": "A Three-parameter Family Of Involutions In The Riordan Group Defined By Orthogonal Polynomials",
  "authors": [
    "Paul Barry"
  ],
  "comment": "9 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We show how to define, for every Riordan group element $(g(x), f(x))$, an involution in the Riordan group. More generally, we show that for every pseudo-involution $P$ in the Riordan group, we can define a new involution beginning with an arbitrary element $(g(x), f(x))$ in the Riordan group. We then use this result to show that certain two-parameter families of orthogonal polynomials defined by a Riordan array can lead to involutions in the Riordan group, and we give an explicit form of these involutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-06T14:45:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05A05",
      "05A19",
      "11B83"
    ],
    "keywords": [
      "orthogonal polynomials",
      "three-parameter family",
      "riordan group element",
      "explicit form",
      "riordan array"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}