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arXiv · 2403.11170

Common substring with shifts in b-ary expansions

Xin Liao·Dingding Yu
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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.

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Xin Liao, Dingding Yu. 2024-03-17. Common substring with shifts in b-ary expansions. https://arxiv.org/abs/2403.11170

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