{
  "id": "1008.0310",
  "version": "v1",
  "published": "2010-08-02T14:09:55.000Z",
  "updated": "2010-08-02T14:09:55.000Z",
  "title": "Interlacing Log-concavity of the Boros-Moll Polynomials",
  "authors": [
    "William Y. C. Chen",
    "Larry X. W. Wang",
    "Ernest X. W. Xia"
  ],
  "comment": "10 pages",
  "categories": [
    "math.CO",
    "math.CA"
  ],
  "abstract": "We introduce the notion of interlacing log-concavity of a polynomial sequence $\\{P_m(x)\\}_{m\\geq 0}$, where $P_m(x)$ is a polynomial of degree m with positive coefficients $a_{i}(m)$. This sequence of polynomials is said to be interlacing log-concave if the ratios of consecutive coefficients of $P_m(x)$ interlace the ratios of consecutive coefficients of $P_{m+1}(x)$ for any $m\\geq 0$. Interlacing log-concavity is stronger than the log-concavity. We show that the Boros-Moll polynomials are interlacing log-concave. Furthermore we give a sufficient condition for interlacing log-concavity which implies that some classical combinatorial polynomials are interlacing log-concave.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-08-02T14:09:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A20",
      "33F10"
    ],
    "keywords": [
      "interlacing log-concavity",
      "boros-moll polynomials",
      "interlacing log-concave",
      "consecutive coefficients",
      "polynomial sequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.0310C"
    }
  }
}