The Zarankiewicz problem through linear hypergraphs and designs

通过线性超图和设计解决 Zarankiewicz 问题

• 批准号: DP220102212
• 负责人: A/Prof Daniel Horsley
• 金额: $ 23.61万
• 依托单位: Monash University
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2022
• 资助国家: 澳大利亚
• 起止时间: 2022-10-01 至 2025-09-30
• 项目状态: 未结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP220102212
• 关键词: Zarankiewicz; problem; through; linear; hypergraphs

The Zarankiewicz problem is a famous open problem with deep connections to many different areas of mathematics. Despite continued attention from some of the world's most celebrated mathematicians, it has remained unsolved for over 70 years. This project aims to make major progress on the Zarankiewicz problem by utilising a novel approach based in the field of combinatorial design theory. This approach will leverage recent major breakthroughs in design theory concerning edge decompositions of dense hypergraphs.

扎兰凯维奇问题是一个著名的开放问题，与许多不同的数学领域有着深刻的联系。尽管世界上一些最著名的数学家持续关注这个问题，但 70 多年来这个问题一直没有得到解决。该项目旨在通过利用基于组合设计理论领域的新方法在 Zarankiewicz 问题上取得重大进展。这种方法将利用有关密集超图边缘分解的设计理论的最新重大突破。