{
  "id": "1410.5628",
  "version": "v1",
  "published": "2014-10-21T12:05:22.000Z",
  "updated": "2014-10-21T12:05:22.000Z",
  "title": "Arithmetic Properties of Partition Quadruples With Odd Parts Distinct",
  "authors": [
    "Liuquan Wang"
  ],
  "comment": "10 pages",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "Let $\\mathrm{pod}_{-4}(n)$ denote the number of partition quadruples of $n$ where the odd parts in each partition are distinct. We find many arithmetic properties of $\\mathrm{pod}_{-4}(n)$ involving the following infinite family of congruences: for any integers $\\alpha \\ge 1$ and $n \\ge 0$, \\[\\mathrm{pod}_{-4}\\Big({{3}^{\\alpha +1}}n+\\frac{5\\cdot {{3}^{\\alpha }}+1}{2}\\Big)\\equiv 0 \\pmod{9}.\\] We also establish some internal congruences and some congruences modulo 2, 5 and 8 satisfied by $\\mathrm{pod}_{-4}(n)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-21T12:05:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A17",
      "11P83"
    ],
    "keywords": [
      "odd parts distinct",
      "partition quadruples",
      "arithmetic properties",
      "internal congruences",
      "congruences modulo"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}