{
  "id": "1806.02316",
  "version": "v1",
  "published": "2018-06-06T17:34:17.000Z",
  "updated": "2018-06-06T17:34:17.000Z",
  "title": "Set partitions without blocks of certain sizes",
  "authors": [
    "Joshua Culver",
    "Andreas Weingartner"
  ],
  "comment": "12 pages, 3 tables",
  "categories": [
    "math.CO"
  ],
  "abstract": "We give an asymptotic estimate for the number of partitions of a set of $n$ elements, whose block sizes avoid a given set $\\mathcal{S}$ of natural numbers. As an application, we derive an estimate for the number of partitions of a set with $n$ elements, which have the property that its blocks can be combined to form subsets of any size between $1$ and $n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-06T17:34:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A18",
      "05A16"
    ],
    "keywords": [
      "set partitions",
      "block sizes avoid",
      "asymptotic estimate",
      "form subsets",
      "natural numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}