{
  "id": "math/0703266",
  "version": "v1",
  "published": "2007-03-09T13:59:18.000Z",
  "updated": "2007-03-09T13:59:18.000Z",
  "title": "Partitions weighted by the parity of the crank",
  "authors": [
    "Dohoon Choi",
    "Soon-Yi Kang",
    "Jeremy Lovejoy"
  ],
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "A partition statistic ` crank' gives combinatorial interpretations for Ramanujan's famous partition congruences. In this paper, we establish an asymptotic formula, Ramanujan type congruences, and q-series identities that the number of partitions with even crank $M_e(n)$ minus the number of partitions with odd crank $M_o(n)$ satisfies. For example, we show that $M_e(5n+4)-M_o(5n+4)\\equiv 0 \\pmod 5.$ We also determine the exact values of $M_e(n)-M_o(n)$ in case of partitions into distinct parts, which are at most two and zero for infinitely many $n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-03-09T13:59:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11P81",
      "11P82",
      "11P83",
      "05A17",
      "33D15",
      "11F11"
    ],
    "keywords": [
      "partitions",
      "ramanujans famous partition congruences",
      "ramanujan type congruences",
      "distinct parts",
      "exact values"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......3266C"
    }
  }
}