{
  "id": "2102.11194",
  "version": "v1",
  "published": "2021-02-22T17:19:04.000Z",
  "updated": "2021-02-22T17:19:04.000Z",
  "title": "The algebraic difference of central Cantor sets and self-similar Cantor sets",
  "authors": [
    "Piotr Nowakowski"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "Let $C(a),C(b)\\subset [0,1]$ be the central Cantor sets generated by sequences $a,b \\in (0,1)^{\\mathbb{N}}$. The main result in the first part of the paper gives a necessary condition and a sufficient condition for sequences $a$ and $b$ which inform when $C(a)-C(b)$ is equal to $[-1,1]$ or is a finite union of closed intervals. In the second part we investigate some self-similar Cantor sets $C(l,r,p)$, which we call S-Cantor sets, generated by numbers $l,r,p \\in \\mathbb{N}$, $l+r<p$. We give a full characterization of the set $C(l_1,r_1,p)-C(l_2,r_2,p)$ which can take one of the form: the interval $[-1,1]$, a Cantor set, an L-Cantorval, an R-Cantorval or an M-Cantorval.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-22T17:19:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A80",
      "05B10",
      "11A67"
    ],
    "keywords": [
      "central cantor sets",
      "self-similar cantor sets",
      "algebraic difference",
      "main result",
      "first part"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}