{
  "id": "math/0605474",
  "version": "v2",
  "published": "2006-05-17T13:14:36.000Z",
  "updated": "2006-05-17T22:49:37.000Z",
  "title": "BG-ranks and 2-cores",
  "authors": [
    "William Y. C. Chen",
    "Kathy Q. Ji",
    "Herbert S. Wilf"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We find the number of partitions of $n$ whose BG-rank is $j$, in terms of $pp(n)$, the number of pairs of partitions whose total number of cells is $n$, giving both bijective and generating function proofs. Next we find congruences mod 5 for $pp(n)$, and then we use these to give a new proof of a refined system of congruences for $p(n)$ that was found by Berkovich and Garvan.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-05-17T22:49:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A17",
      "05A15"
    ],
    "keywords": [
      "total number",
      "generating function proofs",
      "partitions",
      "congruences mod"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......5474C"
    }
  }
}