{
  "id": "1608.07635",
  "version": "v1",
  "published": "2016-08-27T00:16:37.000Z",
  "updated": "2016-08-27T00:16:37.000Z",
  "title": "Random sets and intersections",
  "authors": [
    "David Handelman"
  ],
  "comment": "Comments solicited",
  "categories": [
    "math.PR"
  ],
  "abstract": "The following class of problems arose out of vain attempts to show that the Pascal's triangle adic transformation has trivial spectrum. Partition a set of size $N$ into sets of size $S \\equiv S(N)$ (ignoring leftovers). What is the likelihood that a set of size $K \\equiv K(N)$ will intersect each set in the partition in at least $R \\equiv R(N)$ members (as $N$ increases)? Via elementary techniques and under reasonable hypotheses, we obtain an easy-to-use formula. Although different from the corresponding minimum problem for balls and bins (with $m = K$ balls and $n = N/S$ bins), under modest constraints, the asymptotic probabilities are the same.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-27T00:16:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60C05",
      "05A16"
    ],
    "keywords": [
      "random sets",
      "pascals triangle adic transformation",
      "intersections",
      "vain attempts",
      "trivial spectrum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}