{
  "id": "2207.03661",
  "version": "v1",
  "published": "2022-07-08T02:52:31.000Z",
  "updated": "2022-07-08T02:52:31.000Z",
  "title": "Combinatorial meaning of the number of the even parts in a partition of $n$ into distinct parts",
  "authors": [
    "Jiyou Li",
    "Sicheng Zhao"
  ],
  "comment": "5 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In a recent paper, Andrews and Merca investigated the number of even parts in all partitions of $n$ into distinct parts, which arise naturally from the Euler-Glaisher bijective proof. They obtained new combinatorial interpretations for this number by using generating functions. We obtain a new direct combinatorial proof in this note.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-08T02:52:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A17",
      "11P83"
    ],
    "keywords": [
      "distinct parts",
      "combinatorial meaning",
      "direct combinatorial proof",
      "euler-glaisher bijective proof",
      "combinatorial interpretations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}