The density of planar sets avoiding unit distances

• 成果类型: Article
• 署名作者: Ambrus, Gergely; Csiszarik, Adrian; Matolcsi, Mate; Varga, Daniel; Zsamboki, Pal
• 署名单位: Szeged University; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Eotvos Lorand University; Budapest University of Technology & Economics
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-023-02012-9
• 发表日期: 2024
• 页码: 303-327
• 关键词: chromatic number; realization

摘要

By improving upon previous estimates on a problem posed by L. Moser, we prove a conjecture of Erdos that the density of any measurable planar set avoiding unit distances is less than 1/4. Our argument implies the upper bound of 0.2470.