b-ary 扩展中带有移位的共同子串

IF 0.5 4区数学 Q3 MATHEMATICS

Archiv der Mathematik Pub Date : 2024-08-08 DOI:10.1007/s00013-024-02038-1

Xin Liao, Dingding Yu

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引用次数: 0

摘要

用 \(S_n(x,y)\)表示 x 和 y 的最长公共子串的长度，它们的 b-ary 展开的前 n 位有移位。我们证明，对于\(S_n(x,y)\)的增长率为\(\alpha \log n\) with \(0 \le \alpha \le \infty \)的成对集合（x, y），具有全豪斯多夫维。我们的方法依赖于对矩阵谱半径的一些估计。

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Common substring with shifts in b-ary expansions

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 the 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. Our method relies upon some estimation of the spectral radius of matrices.

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来源期刊

Archiv der Mathematik 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

117

审稿时长

4-8 weeks

期刊介绍： Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.