{
  "id": "1209.5764",
  "version": "v2",
  "published": "2012-09-25T20:55:37.000Z",
  "updated": "2012-10-11T15:36:32.000Z",
  "title": "Threshold functions for distinct parts: revisiting Erdos-Lehner",
  "authors": [
    "Éva Czabarka",
    "Matteo Marsili",
    "László Székely"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We study four problems: put $n$ distinguishable/non-distinguishable balls into $k$ non-empty distinguishable/non-distinguishable boxes randomly. What is the threshold function $k=k(n) $ to make almost sure that no two boxes contain the same number of balls? The non-distinguishable ball problems are very close to the Erd\\H os--Lehner asymptotic formula for the number of partitions of the integer $n$ into $k$ parts with $k=o(n^{1/3})$. The problem is motivated by the statistics of an experiment, where we only can tell whether outcomes are identical or different.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-10-11T15:36:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A17",
      "05A18",
      "05A16",
      "05D40"
    ],
    "keywords": [
      "threshold function",
      "distinct parts",
      "revisiting erdos-lehner",
      "os-lehner asymptotic formula",
      "boxes contain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.5764C"
    }
  }
}