{
  "id": "2001.08931",
  "version": "v1",
  "published": "2020-01-24T09:42:32.000Z",
  "updated": "2020-01-24T09:42:32.000Z",
  "title": "Distribution of missing differences in diffsets",
  "authors": [
    "Scott Harvey-Arnold",
    "Steven J. Miller",
    "Fei Peng"
  ],
  "comment": "Version 1.0, 17 pages, 3 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Lazarev, Miller and O'Bryant investigated the distribution of $|S+S|$ for $S$ chosen uniformly at random from $\\{0, 1, \\dots, n-1\\}$, and proved the existence of a divot at missing 7 sums (the probability of missing exactly 7 sums is less than missing 6 or missing 8 sums). We study related questions for $|S-S|$, and shows some divots from one end of the probability distribution, $P(|S-S|=k)$, as well as a peak at $k=4$ from the other end, $P(2n-1-|S-S|=k)$. A corollary of our results is an asymptotic bound for the number of complete rulers of length $n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-24T09:42:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11P99",
      "11K99"
    ],
    "keywords": [
      "missing differences",
      "asymptotic bound",
      "probability distribution",
      "study related questions",
      "complete rulers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}