{
  "id": "0807.2629",
  "version": "v1",
  "published": "2008-07-16T19:06:14.000Z",
  "updated": "2008-07-16T19:06:14.000Z",
  "title": "Divisibility by 2 and 3 of certain Stirling numbers",
  "authors": [
    "Donald M Davis"
  ],
  "comment": "35 pages, submitted",
  "categories": [
    "math.NT",
    "math.AT"
  ],
  "abstract": "The numbers e_p(k,n) defined as min(nu_p(S(k,j)j!): j >= n) appear frequently in algebraic topology. Here S(k,j) is the Stirling number of the second kind, and nu_p(-) the exponent of p. The author and Sun proved that if L is sufficiently large, then e_p((p-1)p^L + n -1, n) >= n-1+nu_p([n/p]!). In this paper, we determine the set of integers n for which equality holds in this inequality when p=2 and 3. The condition is roughly that, in the base-p expansion of n, the sum of two consecutive digits must always be less than p.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-07-16T19:06:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B73",
      "55Q52"
    ],
    "keywords": [
      "stirling number",
      "divisibility",
      "algebraic topology",
      "second kind",
      "equality holds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.2629D"
    }
  }
}