{
  "id": "1308.2452",
  "version": "v4",
  "published": "2013-08-12T03:10:32.000Z",
  "updated": "2014-06-22T22:06:29.000Z",
  "title": "Block Partitions of Sequences",
  "authors": [
    "Imre Bárány",
    "Victor S. Grinberg"
  ],
  "comment": "9 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Given a sequence A=(a1,...,an) of real numbers, a block B of the A is either a set B={ai,...,aj} where i<=j or the empty set. The size b of a block B is the sum of its elements. We show that when 0<=ai<=1 and k is a positive integer, there is a partition of A into k blocks B1,...,Bk with |bi-bj|<=1 for every i, j. We extend this result in many directions.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2014-06-22T22:06:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05A18"
    ],
    "keywords": [
      "block partitions",
      "real numbers",
      "empty set",
      "blocks b1"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.2452B"
    }
  }
}