Common substring with shifts in b-ary expansions

被引：0
|
作者：
Liao, Xin [1 ]
Yu, Dingding [1 ]
机构：
[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China
来源：
ARCHIV DER MATHEMATIK | 2024年 / 123卷 / 04期
关键词：
b-ary expansions; Common substring with shifts; Hausdorff dimension;
D O I：
10.1007/s00013-024-02038-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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 <= alpha <= infinity, have full Hausdorff dimension. Our method relies upon some estimation of the spectral radius of matrices.
引用
收藏
页码：369 / 377
页数：9
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