A proof of the Erd\"os similarity conjecture

Angel Cruz; Chun-Kit Lai; Malabika Pramanik

A proof of the Erd\"os similarity conjecture

Classical Analysis and ODEs 2020-01-14 v2 Combinatorics

Authors: Angel Cruz , Chun-Kit Lai , Malabika Pramanik

Abstract

We show that for any infinite set $A$ in ${\mathbb R}$ , there exists a compact set $E \subseteq \mathbb{R}$ of positive Lebesgue measure that does not contain any non-trivial affine copy of $A$ . This proves the Erd\"os similarity conjecture.

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@article{arxiv.2001.02395,
  title  = {A proof of the Erd\"os similarity conjecture},
  author = {Angel Cruz and Chun-Kit Lai and Malabika Pramanik},
  journal= {arXiv preprint arXiv:2001.02395},
  year   = {2020}
}

Comments

A gap was found in Proposition 3.3 of the paper. We would like to thank professor Vjekoslav Kovac for pointing this out. Therefore, we would like to withdraw the paper

A proof of the Erd\"os similarity conjecture

Abstract

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