{
  "id": "2107.08436",
  "version": "v1",
  "published": "2021-07-18T13:02:27.000Z",
  "updated": "2021-07-18T13:02:27.000Z",
  "title": "Yet another criterion for the total positivity of Riordan arrays",
  "authors": [
    "Jianxi Mao",
    "Lili Mu",
    "Yi Wang"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $R=\\mathcal{R}(d(t),h(t))$ be a Riordan array, where $d(t)=\\sum_{n\\ge 0}d_nt^n$ and $h(t)=\\sum_{n\\ge 0}h_nt^n$. We show that if the matrix \\begin{equation*} \\left[\\begin{array}{ccccc} d_0 & h_0 & 0 & 0 &\\cdots\\\\ d_1 & h_1 & h_0 & 0 &\\\\ d_2 & h_2 & h_1 & h_0 &\\\\ \\vdots&\\vdots&&&\\ddots \\end{array}\\right] \\end{equation*} is totally positive, then so is the Riordan array $R$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-18T13:02:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15B48",
      "15B36",
      "15B05"
    ],
    "keywords": [
      "riordan array",
      "total positivity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}