{
  "id": "1706.03020",
  "version": "v1",
  "published": "2017-06-09T16:22:36.000Z",
  "updated": "2017-06-09T16:22:36.000Z",
  "title": "Modular Forms and $k$-colored Generalized Frobenius Partitions",
  "authors": [
    "Heng Huat Chan",
    "Liuquan Wang",
    "Yifan Yang"
  ],
  "comment": "45 pages",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "Let $k$ and $n$ be positive integers. Let $c\\phi_{k}(n)$ denote the number of $k$-colored generalized Frobenius partitions of $n$ and $\\mathrm{C}\\Phi_k(q)$ be the generating function of $c\\phi_{k}(n)$. In this article, we study $\\mathrm{C}\\Phi_k(q)$ using the theory of modular forms and discover new surprising properties of $\\mathrm{C}\\Phi_k(q)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-09T16:22:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A17",
      "11F11",
      "11P83",
      "11F03",
      "11F33"
    ],
    "keywords": [
      "colored generalized frobenius partitions",
      "modular forms",
      "generating function",
      "surprising properties",
      "positive integers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}