{
  "id": "1906.00680",
  "version": "v1",
  "published": "2019-06-03T10:04:50.000Z",
  "updated": "2019-06-03T10:04:50.000Z",
  "title": "Sum of weighted records in set partitions",
  "authors": [
    "Walaa Asakly"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "The purpose of this paper is to find an explicit formula and asymptotic estimate for the total number of sum of weighted records over set partitions of $[n]$ in terms of Bell numbers. For that we study the generating function for the number of set partitions of $[n]$ according to the statistic sum of weighted records.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-03T10:04:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A05",
      "05A15",
      "05A17"
    ],
    "keywords": [
      "set partitions",
      "weighted records",
      "statistic sum",
      "total number",
      "explicit formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}