{
  "id": "2403.11170",
  "version": "v1",
  "published": "2024-03-17T11:05:42.000Z",
  "updated": "2024-03-17T11:05:42.000Z",
  "title": "Common substring with shifts in b-ary expansions",
  "authors": [
    "Xin Liao",
    "Dingding Yu"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Denote by $S_n(x,y)$ the length of the longest common substring of $x$ and $y$ with shifts in their first $n$ digits of $b$-ary expansions. We show that the sets of pairs $(x,y)$, for which the growth rate of $S_n(x,y)$ is $\\alpha \\log n$ with $0\\le \\alpha \\le \\infty$, have full Hausdorff dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-17T11:05:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "b-ary expansions",
      "full hausdorff dimension",
      "growth rate",
      "longest common substring"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}