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Given a sequence $\{b_{i}\}_{i=1}^{n}$ and a ratio $\lambda \in (0,1),$ let $E=\cup_{i=1}^n(\lambda E+b_i)$ be a homogeneous self-similar set. In this paper, we study the existence and maximal length of arithmetic… Click to show full abstract
Given a sequence $\{b_{i}\}_{i=1}^{n}$ and a ratio $\lambda \in (0,1),$ let $E=\cup_{i=1}^n(\lambda E+b_i)$ 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.
Keywords:
self similar;
similar sets;
progressions self;
arithmetic progressions
Journal Title: Frontiers of Mathematics in China
Year Published: 2019
Link to full text (if available)
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Journal Title: Frontiers of Mathematics in China
Year Published: 2019
Link to full text (if available)
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recommendations!