{
  "id": "1001.1783",
  "version": "v3",
  "published": "2010-01-12T02:49:44.000Z",
  "updated": "2011-03-20T19:01:48.000Z",
  "title": "The number of nonzero binomial coefficients modulo p^alpha",
  "authors": [
    "Eric Rowland"
  ],
  "comment": "10 pages; publication version",
  "journal": "Journal of Combinatorics and Number Theory 3 (2011) 15-25",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "In 1947 Fine obtained an expression for the number of binomial coefficients on row n of Pascal's triangle that are nonzero modulo p. In this paper we use Kummer's theorem to generalize Fine's theorem to prime powers, expressing the number of nonzero binomial coefficients modulo p^alpha as a sum over certain integer partitions. For fixed alpha, this expression can be rewritten to show explicit dependence on the number of occurrences of each subword in the base-p representation of n.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-03-20T19:01:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B65",
      "11A63",
      "05A17",
      "05A15"
    ],
    "keywords": [
      "nonzero binomial coefficients modulo",
      "expression",
      "base-p representation",
      "explicit dependence",
      "pascals triangle"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1001.1783R"
    }
  }
}