{
  "id": "2301.09546",
  "version": "v1",
  "published": "2023-01-23T17:03:56.000Z",
  "updated": "2023-01-23T17:03:56.000Z",
  "title": "Characterization of the algebraic difference of special affine Cantor sets",
  "authors": [
    "Piotr Nowakowski"
  ],
  "comment": "This paper was previously a part of the submission arXiv:2102.11194v1",
  "categories": [
    "math.CA"
  ],
  "abstract": "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. As corollaries we give examples of Cantor sets and Cantorvals, which can be easily described using some positional numeral systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-23T17:03:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A80",
      "05B10",
      "11A67"
    ],
    "keywords": [
      "special affine cantor sets",
      "algebraic difference",
      "self-similar cantor sets",
      "positional numeral systems",
      "s-cantor sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}