Arithmetic progressions in self-similar sets

被引：0
作者：
Xi, Lifeng [1 ]
Jiang, Kan [1 ]
Pei, Qiyang [1 ]
机构：
[1] Ningbo Univ, Dept Math, Ningbo 315211, Peoples R China
来源：
FRONTIERS OF MATHEMATICS IN CHINA | 2019年 / 14卷 / 05期
基金：
中国国家自然科学基金;
关键词：
Self-similar sets; arithmetic progression (AP); beta-expansions; REAL NUMBERS; DIMENSION; EXPANSIONS;
D O I：
10.1007/s11464-019-0788-2
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Given a sequence {b(i)}(i=1)(n) and a ratio lambda is an element of (0, 1), let E = boolean OR(n)(i=1) (lambda E+b(i)) be a homogeneous self-similar set. In this paper, we study the existence and maximal length of arithmetic progressions in E: Our main idea is from the multiple beta-expansions.
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页码：957 / 966
页数：10
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