{
  "id": "1009.5016",
  "version": "v1",
  "published": "2010-09-25T14:21:33.000Z",
  "updated": "2010-09-25T14:21:33.000Z",
  "title": "Arithmetic Properties of Overpartition Pairs",
  "authors": [
    "William Y. C. Chen",
    "Bernard L. S. Lin"
  ],
  "comment": "19 pages",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "Bringmann and Lovejoy introduced a rank for overpartition pairs and investigated its role in congruence properties of $\\bar{pp}(n)$, the number of overpartition pairs of n. In particular, they applied the theory of Klein forms to show that there exist many Ramanujan-type congruences for the number $\\bar{pp}(n)$. In this paper, we shall derive two Ramanujan-type identities and some explicit congruences for $\\bar{pp}(n)$. Moreover, we find three ranks as combinatorial interpretations of the fact that $\\bar{pp}(n)$ is divisible by three for any n. We also construct infinite families of congruences for $\\bar{pp}(n)$ modulo 3, 5, and 9.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-09-25T14:21:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A17",
      "11P83"
    ],
    "keywords": [
      "overpartition pairs",
      "arithmetic properties",
      "construct infinite families",
      "congruence properties",
      "combinatorial interpretations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.5016C"
    }
  }
}