{
  "id": "1601.05645",
  "version": "v1",
  "published": "2016-01-21T14:12:15.000Z",
  "updated": "2016-01-21T14:12:15.000Z",
  "title": "Total positivity of recursive matrices",
  "authors": [
    "Xi Chen",
    "Huyile Liang",
    "Yi Wang"
  ],
  "journal": "Linear Algebra Appl. 471(2015) 383--393",
  "doi": "10.1016/j.laa.2015.01.009",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $A=[a_{n,k}]_{n,k\\ge 0}$ be an infinite lower triangular matrix defined by the recurrence $$a_{0,0}=1,\\quad a_{n+1,k}=r_{k}a_{n,k-1}+s_{k}a_{n,k}+t_{k+1}a_{n,k+1},$$ where $a_{n,k}=0$ unless $n\\ge k\\ge 0$ and $r_k,s_k,t_k$ are all nonnegative. Many well-known combinatorial triangles are such matrices, including the Pascal triangle, the Stirling triangle (of the second kind), the Bell triangle, the Catalan triangles of Aigner and Shapiro. We present some sufficient conditions such that the recursive matrix $A$ is totally positive. As applications we give the total positivity of the above mentioned combinatorial triangles in a unified approach.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-21T14:12:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A20",
      "15B36",
      "15A45"
    ],
    "keywords": [
      "total positivity",
      "recursive matrix",
      "infinite lower triangular matrix",
      "well-known combinatorial triangles",
      "sufficient conditions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160105645C"
    }
  }
}