{
  "id": "0901.0385",
  "version": "v1",
  "published": "2009-01-04T15:45:16.000Z",
  "updated": "2009-01-04T15:45:16.000Z",
  "title": "Confirming Two Conjectures of Su and Wang",
  "authors": [
    "Yaming Yu"
  ],
  "comment": "8 pages, 1 figure, tentatively accepted by adv. in appl. math",
  "journal": "Adv. in Appl. Math. 43 (2009) 317--322",
  "doi": "10.1016/j.aam.2008.12.004",
  "categories": [
    "math.CO",
    "math.CA"
  ],
  "abstract": "Two conjectures of Su and Wang (2008) concerning binomial coefficients are proved. For $n\\geq k\\geq 0$ and $b>a>0$, we show that the finite sequence $C_j=\\binom{n+ja}{k+jb}$ is a P\\'{o}lya frequency sequence. For $n\\geq k\\geq 0$ and $a>b>0$, we show that there exists an integer $m\\geq 0$ such that the infinite sequence $\\binom{n+ja}{k+jb}, j=0, 1,...$, is log-concave for $0\\leq j\\leq m$ and log-convex for $j\\geq m$. The proof of the first result exploits the connection between total positivity and planar networks, while that of the second uses a variation-diminishing property of the Laplace transform.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-01-04T15:45:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A10",
      "05A20"
    ],
    "keywords": [
      "conjectures",
      "first result exploits",
      "infinite sequence",
      "confirming",
      "frequency sequence"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0901.0385Y"
    }
  }
}