{
  "id": "1502.00938",
  "version": "v1",
  "published": "2015-02-03T17:34:09.000Z",
  "updated": "2015-02-03T17:34:09.000Z",
  "title": "Central Limit Theorems for some Set Partition Statistics",
  "authors": [
    "Bobbie Chern",
    "Persi Diaconis",
    "Daniel M. Kane",
    "Robert C. Rhoades"
  ],
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "We prove the conjectured limiting normality for the number of crossings of a uniformly chosen set partition of [n] = {1,2,...,n}. The arguments use a novel stochastic representation and are also used to prove central limit theorems for the dimension index and the number of levels.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-03T17:34:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A18",
      "05A16",
      "60C05"
    ],
    "keywords": [
      "central limit theorems",
      "set partition statistics",
      "uniformly chosen set partition",
      "novel stochastic representation",
      "dimension index"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150200938C"
    }
  }
}