{
  "id": "1706.06095",
  "version": "v1",
  "published": "2017-06-18T21:40:16.000Z",
  "updated": "2017-06-18T21:40:16.000Z",
  "title": "Block partitions: an extended view",
  "authors": [
    "I. Bárány",
    "E. Csóka",
    "Gy. Károlyi",
    "G. Tóth"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Given a sequence $S=(s_1,\\dots,s_m) \\in [0, 1]^m$, a block $B$ of $S$ is a subsequence $B=(s_i,s_{i+1},\\dots,s_j)$. The size $b$ of a block $B$ is the sum of its elements. It is proved in [1] that for each positive integer $n$, there is a partition of $S$ into $n$ blocks $B_1, \\dots , B_n$ with $|b_i - b_j| \\le 1$ for every $i, j$. In this paper, we consider a generalization of the problem in higher dimensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-18T21:40:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "block partitions",
      "extended view",
      "higher dimensions",
      "generalization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}