{
  "id": "1310.0353",
  "version": "v2",
  "published": "2013-10-01T15:42:45.000Z",
  "updated": "2013-10-07T13:00:21.000Z",
  "title": "Inequalities for binomial coefficients",
  "authors": [
    "Zhi-Hong Sun"
  ],
  "comment": "10 pages",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "In this paper we prove several inequalities for binomial coefficients. For instance, if $ k$ and $n$ are positive integers such that $n\\ge 400$ and $[\\frac n5]\\le k\\le [\\frac n2]$, where $[x]$ is the greatest integer not exceeding $x$, then $$\\binom nk<\\Big(1-\\frac{5(k-[\\f n5])}{6n^2}\\Big) \\frac{n^{n-\\f 12}}{k^k(n-k)^{n-k}}.$$",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-10-07T13:00:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A20",
      "11B65",
      "33B15"
    ],
    "keywords": [
      "binomial coefficients",
      "inequalities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.0353S"
    }
  }
}