{
  "id": "2004.09505",
  "version": "v1",
  "published": "2020-04-20T10:05:54.000Z",
  "updated": "2020-04-20T10:05:54.000Z",
  "title": "A Complete Solution of the Partitions of a Number into Arithmetic Progressions",
  "authors": [
    "F. Javier de Vega"
  ],
  "comment": "9 pages; added notes for helping the referee. arXiv admin note: text overlap with arXiv:2003.13378",
  "categories": [
    "math.NT"
  ],
  "abstract": "The paper solves the enumeration of the set AP($n$) of partitions of a positive integer $n$ in which the nondecreasing sequence of parts form an arithmetic progression. In particular, we prove a formula for the number of arithmetic progressions of positive, integers, nondecreasing with sum $n$. We also present an explicit method to calculate all the partitions of AP($n$).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-20T10:05:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11P81"
    ],
    "keywords": [
      "arithmetic progression",
      "complete solution",
      "partitions",
      "explicit method",
      "set ap"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}