{
  "id": "2308.14514",
  "version": "v1",
  "published": "2023-08-28T12:02:58.000Z",
  "updated": "2023-08-28T12:02:58.000Z",
  "title": "A Decomposition of Cylindric Partitions and Cylindric Partitions into Distinct Parts",
  "authors": [
    "Kağan Kurşungöz",
    "Halime Ömrüuzun Seyrek"
  ],
  "comment": "44 pages, 50+ figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We show that cylindric partitions are in one-to-one correspondence with a pair which has an ordinary partition and a colored partition into distinct parts. Then, we show the general form of the generating function for cylindric partitions into distinct parts and give some examples. We prove part of a conjecture by Corteel, Dousse, and Uncu. With due computational support; the other part of Corteel, Dousse, and Uncu's conjecture, which also appeared in Warnaar's work, is extended. The approaches and proofs are elementary and combinatorial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-28T12:02:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A17",
      "05A15",
      "11P84"
    ],
    "keywords": [
      "cylindric partitions",
      "distinct parts",
      "decomposition",
      "general form",
      "ordinary partition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}