{
  "id": "2407.07891",
  "version": "v1",
  "published": "2024-07-10T17:58:03.000Z",
  "updated": "2024-07-10T17:58:03.000Z",
  "title": "A proposed crank for $(k+j)$-colored partitions, with $j$ colors having distinct parts",
  "authors": [
    "Samuel Wilson"
  ],
  "comment": "6 pages, 1 table",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "In 1988, George Andrews and Frank Garvan discovered a crank for $p(n)$. In 2020, Larry Rolen, Zack Tripp, and Ian Wagner generalized the crank for p(n) in order to accommodate Ramanujan-like congruences for $k$-colored partitions. In this paper, we utilize the techniques used by Rolen, Tripp, and Wagner for crank generating functions in order to define a crank generating function for $(k + j)$-colored partitions where $j$ colors have distinct parts. We provide three infinite families of crank generating functions and conjecture a general crank generating function for such partitions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-10T17:58:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A15",
      "05A17"
    ],
    "keywords": [
      "colored partitions",
      "distinct parts",
      "general crank generating function",
      "frank garvan",
      "zack tripp"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}