Arithmetic progressions in self-similar sets  

作　　者：Lifeng XI Kan JIANG Qiyang PEI 

机构地区：[1]Department of Mathematics,Ningbo University,Ningbo 315211,China

出　　处：《Frontiers of Mathematics in China》2019年第5期957-966,共10页中国高等学校学术文摘·数学（英文）

基　　金：This work was supported by the National Natural Science Foundation of China(Grant Nos.11831007,11771226,11701302,11371329,11471124,11671147);the K.C.Wong Magna Fund in Ningbo University.

摘　　要：Given a sequence{bi}i=1^n and a ratio λ∈(0,1),let E=Ui=1^n(λE+bi)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 β-expansions.

关 键 词：SELF-SIMILAR SETS ARITHMETIC PROGRESSION (AP) β-expansions 

分 类 号：O17[理学—数学]