Scholarlink

<p>The Erdős similarity conjecture was proposed by P. Erdős in 1974. The conjecture remains open for exponentially decaying sequences as well as Cantor sets that have both Newhouse thickness and Hausdorff dimension zero. In this article—written 50 years after the conjecture was first proposed—we review progress on some new variants of the original problem, namely the bi-Lipschitz variant, the topological variant, and a variant “in the large”. These problems were recently studied by the authors and their collaborators. Each of them offers new perspectives on the original conjecture.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Fifty years of the Erdős similarity conjecture

  • 期刊论文

  • 发表日期：

    2025年1月16日

查看全文
  • Yeonwook Jung,
  • Chun-Kit Lai,
  • Yuveshen Mooroogen

摘要

The Erdős similarity conjecture was proposed by P. Erdős in 1974. The conjecture remains open for exponentially decaying sequences as well as Cantor sets that have both Newhouse thickness and Hausdorff dimension zero. In this article—written 50 years after the conjecture was first proposed—we review progress on some new variants of the original problem, namely the bi-Lipschitz variant, the topological variant, and a variant “in the large”. These problems were recently studied by the authors and their collaborators. Each of them offers new perspectives on the original conjecture.