Common substring with shifts in b-ary expansions
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913269095071744 |
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| author | Liao, Xin Yu, Dingding |
| author_facet | Liao, Xin Yu, Dingding |
| contents | 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 $α\log n$ with $0\le α\le \infty$, have full Hausdorff dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_11170 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Common substring with shifts in b-ary expansions Liao, Xin Yu, Dingding Number Theory 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 $α\log n$ with $0\le α\le \infty$, have full Hausdorff dimension. |
| title | Common substring with shifts in b-ary expansions |
| topic | Number Theory |
| url | https://arxiv.org/abs/2403.11170 |