{
  "id": "1802.00959",
  "version": "v1",
  "published": "2018-02-03T11:41:17.000Z",
  "updated": "2018-02-03T11:41:17.000Z",
  "title": "Combinatorial proofs for identities related with generalizations of the mock theta functions $ω(q)$ and $ν(q)$",
  "authors": [
    "Frank Z. K. Li",
    "Jane Y. X. Yang"
  ],
  "comment": "21 pages, 6 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The two partition functions $p_\\omega(n)$ and $p_\\nu(n)$ were introduced by Andrews, Dixit and Yee, which are related with the third order mock theta functions $\\omega(q)$ and $\\nu(q)$, respectively. Recently, Andrews and Yee analytically studied two identities that connect the refinements of $p_\\omega(n)$ and $p_\\nu(n)$ with the generalized bivariate mock theta functions $\\omega(z;q)$ and $\\nu(z;q)$, respectively. However, they cried out for bijective proofs of these two identities. In this paper, we first define the generalized trivariate mock theta functions $\\omega(y,z;q)$ and $\\nu(y,z;q)$. Then by utilizing odd Ferrers graph, we obtain certain identities concerning with $\\omega(y,z;q)$ and $\\nu(y,z;q)$, which extend some early results of Andrews that are related with $\\omega(z;q)$ and $\\nu(z;q)$. In virtue of the combinatorial interpretations that arise from the identities involving $\\omega(y,z;q)$ and $\\nu(y,z;q)$, we finally present bijective proofs for the two identities of Andrews-Yee.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-03T11:41:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A17",
      "05A19"
    ],
    "keywords": [
      "identities",
      "combinatorial proofs",
      "third order mock theta functions",
      "generalized bivariate mock theta functions",
      "generalized trivariate mock theta functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}