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.
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.
