{
  "id": "0907.3412",
  "version": "v2",
  "published": "2009-07-20T14:51:34.000Z",
  "updated": "2011-12-27T15:52:24.000Z",
  "title": "The 2-adic valuations of Stirling numbers of the second kind",
  "authors": [
    "Shaofang Hong",
    "Jianrong Zhao",
    "Wei Zhao"
  ],
  "comment": "9 pages. To appear in International Journal of Number Theory",
  "journal": "International J. Number Theory 8 (2012), 1057--1066",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we investigate the 2-adic valuations of the Stirling numbers $S(n, k)$ of the second kind. We show that $v_2(S(4i, 5))=v_2(S(4i+3, 5))$ if and only if $i\\not\\equiv 7\\pmod {32}$. This confirms a conjecture of Amdeberhan, Manna and Moll raised in 2008. We show also that $v_2(S(2^n+1, k+1))= s_2(n)-1$ for any positive integer $n$, where $s_2(n)$ is the sum of binary digits of $n$. It proves another conjecture of Amdeberhan, Manna and Moll.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-12-27T15:52:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B73",
      "11A07"
    ],
    "keywords": [
      "second kind",
      "stirling numbers",
      "valuations",
      "binary digits"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.3412H"
    }
  }
}