{
  "id": "1805.02213",
  "version": "v1",
  "published": "2018-05-06T13:44:54.000Z",
  "updated": "2018-05-06T13:44:54.000Z",
  "title": "Uniform Distribution of Kakutani Partitions Generated By Substitution Schemes",
  "authors": [
    "Yotam Smilansky"
  ],
  "comment": "24 pages, 20 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "The main result of this paper is a proof of uniform distribution for a large family of sequences of partitions, constituting a generalization of a result of Kakutani regarding partitions of the unit interval. A sequence is defined according to a multiscale substitution scheme on a set of prototiles, which is a set of substitution rules determining a tiling of each prototile by rescaled copies of the prototiles at hand. Given a multiscale substitution scheme, a succession of substitutions of tiles is used to define a sequence of partitions, which is studied using a directed weighted graph associated with the scheme.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-06T13:44:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B45",
      "52C23",
      "11K36",
      "60B10",
      "05C21"
    ],
    "keywords": [
      "uniform distribution",
      "kakutani partitions",
      "multiscale substitution scheme",
      "kakutani regarding partitions",
      "unit interval"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}