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arXiv · 1901.06673

On arithmetic progressions in self-similar sets

Kan Jiang·Qiyang Pei·Lifeng Xi
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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.

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Kan Jiang, Qiyang Pei, Lifeng Xi. 2019-01-20. On arithmetic progressions in self-similar sets. https://arxiv.org/abs/1901.06673

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