{
  "id": "1408.4089",
  "version": "v1",
  "published": "2014-08-18T18:20:36.000Z",
  "updated": "2014-08-18T18:20:36.000Z",
  "title": "Restricted k-color partitions",
  "authors": [
    "William J. Keith"
  ],
  "comment": "17 pages. I thank Jeremy Rouse for a particular lemma on MathOverflow",
  "categories": [
    "math.CO"
  ],
  "abstract": "We generalize overpartitions to (k,j)-colored partitions: k-colored partitions in which each part size may have at most j colors. We find numerous congruences and other symmetries. We use a wide array of tools to prove our theorems: generating function dissections, modular forms, bijections, and other combinatorial maps. We find connections to divisor sums, the Han/Nekrasov-Okounkov hook length formula and a possible approach to a finitization, and other topics, suggesting that a rich mine of results is available.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-18T18:20:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A17",
      "11P83"
    ],
    "keywords": [
      "restricted k-color partitions",
      "han/nekrasov-okounkov hook length formula",
      "modular forms",
      "divisor sums",
      "combinatorial maps"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.4089K"
    }
  }
}