On arithmetic progressions in self-similar sets

2019/01/20 by Jiang, Kan, Pei, Qiyang, Xi, Lifeng
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1901.06673

Abstract

Given a sequence \b_i\_i=1ⁿ and a ratio λ∈ (0,1), let E=∪_i=1ⁿ(λE+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 β-expansions.

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