{
  "id": "1404.1883",
  "version": "v2",
  "published": "2014-04-07T19:00:32.000Z",
  "updated": "2014-08-21T19:17:56.000Z",
  "title": "Rank and Crank Moments for Partitions without Repeated Odd Parts",
  "authors": [
    "Chris Jennings-Shaffer"
  ],
  "comment": "to appear in IJNT",
  "categories": [
    "math.NT"
  ],
  "abstract": "Using quasimodular forms with respect to $\\Gamma_0(4)$ we find exact relations between the M2-rank for partitions without repeated odd parts and three residual cranks. From these identities we are able to deduce various congruences mod 3 and 5 between the rank and crank moments. In turn, these congruences give congruences for $M2spt(n)$, the number of occurrences of smallest parts in the partitions of $n$ with smallest part even and without repeated odd parts, and for the higher order analog $M2spt_2(n)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-07T19:00:32.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-08-21T19:17:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "repeated odd parts",
      "crank moments",
      "partitions",
      "smallest part",
      "higher order analog"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.1883J"
    }
  }
}