{
  "id": "2008.10500",
  "version": "v1",
  "published": "2020-08-24T15:05:20.000Z",
  "updated": "2020-08-24T15:05:20.000Z",
  "title": "Asymptotic formulas for the number of the partitions into summands of the form $\\lfloorαm\\rfloor$",
  "authors": [
    "Nian Hong Zhou"
  ],
  "comment": "13 pages",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "Let $\\alpha>1$ be an irrational number. We establish asymptotic formulas for the number of partitions of $n$ into summands and distinct summands, chosen from the sequence $\\{\\lfloor\\alpha m\\rfloor\\}_{m\\in\\mathbb{N}}$. This improves some results of Erd\\\"{o}s and Richmond established in 1977.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-24T15:05:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11P82",
      "05A16",
      "11J82"
    ],
    "keywords": [
      "partitions",
      "distinct summands",
      "irrational number",
      "establish asymptotic formulas"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}