{
  "id": "1504.07156",
  "version": "v1",
  "published": "2015-04-27T16:52:25.000Z",
  "updated": "2015-04-27T16:52:25.000Z",
  "title": "On sums and permutations",
  "authors": [
    "Jakub Konieczny"
  ],
  "comment": "36 pages",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "We study the number of distinct sums $\\sum_{i=u}^v a_i$, where the sequence $a_1,a_2,\\dots,a_n$ is a permutation of $1,2,\\dots,n$, and $u \\leq v$ vary from $1$ to $n$. In particular, we show that generically there are at least $c n^2$ such sums, for a absolute constant $c$. This answers an old question of Erd\\H{o}s and Harheim. We also obtain non-trivial bounds on the maximal possible number of distinct sums, where $n$ is fixed and $a$ is allowed to vary.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-27T16:52:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "permutation",
      "distinct sums",
      "absolute constant",
      "old question"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150407156K"
    }
  }
}