{
  "id": "2001.08351",
  "version": "v1",
  "published": "2020-01-23T02:43:46.000Z",
  "updated": "2020-01-23T02:43:46.000Z",
  "title": "Restricted k-color partitions, II",
  "authors": [
    "William J. Keith"
  ],
  "comment": "9 pages. Submitted to Proceedings of Berndt 80",
  "categories": [
    "math.CO"
  ],
  "abstract": "We consider $(k,j)$-colored partitions, partitions in which $k$ colors exist but at most $j$ colors may be chosen per size of part. In particular these generalize overpartitions. Advancing previous work, we find new congruences, including in previously unexplored cases where $k$ and $j$ are not coprime, as well as some noncongruences. As a useful aside, we give the apparently new generating function for the number of partitions in the $N \\times M$ box with a given number of part sizes, and extend to multiple colors a conjecture of Dousse and Kim on unimodality in overpartitions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-23T02:43:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A17",
      "11P83"
    ],
    "keywords": [
      "restricted k-color partitions",
      "multiple colors",
      "part sizes",
      "unexplored cases",
      "noncongruences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}