{
  "id": "2108.08639",
  "version": "v1",
  "published": "2021-08-19T12:04:11.000Z",
  "updated": "2021-08-19T12:04:11.000Z",
  "title": "Generalizations of Dyson's Rank on Overpartitions",
  "authors": [
    "Alice X. H. Zhao"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We introduce a statistic on overpartitions called the $\\overline{k}$-rank. When there are no overlined parts, this coincides with the $k$-rank of a partition introduced by Garvan. Moreover, it reduces to the D-rank of an overpartition when $k=2$. The generating function for the $\\overline{k}$-rank of overpartitions is given. We also establish a relation between the generating function of self-3-conjugate overpartitions and the tenth order mock theta functions $X(q)$ and $\\chi(q)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-19T12:04:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11P81",
      "05A17",
      "33D15"
    ],
    "keywords": [
      "overpartition",
      "dysons rank",
      "generalizations",
      "order mock theta functions",
      "generating function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}