{
  "id": "2204.07218",
  "version": "v1",
  "published": "2022-04-14T20:43:41.000Z",
  "updated": "2022-04-14T20:43:41.000Z",
  "title": "Number of partitions of n with a given parity of the smallest part",
  "authors": [
    "Damanvir Singh Binner"
  ],
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "We obtain a combinatorial proof of a surprising weighted partition equality of Berkovich and Uncu. Our proof naturally leads to a formula for the number of partitions with a given parity of the smallest part, in terms of S(i), the number of partitions of i into distinct parts with even rank minus the number with odd rank, for which there is an almost closed formula by Andrews, Dyson and Hickerson. This method of calculating the number of partitions of n with a given parity of the smallest part is practical and efficient.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-14T20:43:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "smallest part",
      "surprising weighted partition equality",
      "combinatorial proof",
      "distinct parts",
      "rank minus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}