{
  "id": "1003.1064",
  "version": "v2",
  "published": "2010-03-04T15:47:53.000Z",
  "updated": "2010-04-29T13:07:31.000Z",
  "title": "Congruence properties of the function which counts compositions into powers of 2",
  "authors": [
    "Giedrius Alkauskas"
  ],
  "comment": "8 pages",
  "journal": "Journal of Integer Sequences 13 (2010), Article: 10.5.3, 9 p.",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "Let v(n) denote the number of compositions (ordered partitions) of a positive integer n into powers of 2. It appears that the function v(n) satisfies many congruences modulo 2^N. For example, for every integer B there exists (as k tends to infinity) the limit of v(2^k+B) in the 2-adic topology. The parity of v(n) obeys a simple rule. In this paper we extend this result to higher powers of 2. In particular, we prove that for each positive integer N there exists a finite table which lists all the possible cases of this sequence modulo 2^N. One of our main results claims that v(n) is divisible by 2^N for almost all n, however large the value of N is.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-04-29T13:07:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11P83",
      "11P81",
      "05A17"
    ],
    "keywords": [
      "congruence properties",
      "counts compositions",
      "positive integer",
      "main results claims",
      "simple rule"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.1064A"
    }
  }
}