{
  "id": "1410.7898",
  "version": "v1",
  "published": "2014-10-29T08:27:49.000Z",
  "updated": "2014-10-29T08:27:49.000Z",
  "title": "Arithmetic Properties of Overpartition Triples",
  "authors": [
    "Liuquan Wang"
  ],
  "comment": "14 pages",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "Let ${{\\bar{p}}_{3}}(n)$ be the number of overpartition triples of $n$. We find some congruences for ${\\bar{p}}_{3}(n)$ modulo small powers of 2, such as \\[{{\\bar{p}}_{3}}(16n+14)\\equiv 0 \\pmod{32}, \\quad {{\\bar{p}}_{3}}(8n+7)\\equiv 0 \\pmod{64}.\\] We also establish many arithmetic properties for ${{\\bar{p}}_{3}}(n)$ modulo 7, 9 and 11, involving the following infinite families of Ramanujan-type congruences: for any integers $\\alpha \\ge 1$ and $n \\ge 0$, we have ${{\\bar{p}}_{3}}\\big({{3}^{2\\alpha +1}}(3n+2)\\big)\\equiv 0$ (mod 9) and \\[{{\\bar{p}}_{3}}\\big({{7}^{2\\alpha +1}}(7n+3)\\big)\\equiv {{\\bar{p}}_{3}}\\big({{7}^{2\\alpha +1}}(7n+5)\\big)\\equiv {{\\bar{p}}_{3}}\\big({{7}^{2\\alpha +1}}(7n+6)\\big)\\equiv 0 \\pmod{7}.\\]",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-29T08:27:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A17",
      "11P83"
    ],
    "keywords": [
      "overpartition triples",
      "arithmetic properties",
      "modulo small powers",
      "infinite families",
      "ramanujan-type congruences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.7898W"
    }
  }
}