Sumsets in sets of positive density

正密度集中的总和

• 批准号: EP/V050362/1
• 负责人: Donald Robertson
• 金额: $ 2.58万
• 依托单位: University of Manchester
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FV050362%2F1
• 关键词: Sumsets; sets; positive; density

A central theme in the mathematical field of arithmetic combinatorics is the extent to which size alone can guarantee additive structure. A typical question along these lines is: for which arithmetic patterns is it the case that any large enough collection of numbers is guaranteed to contain a copy of the pattern? The goal of the proposed research is to push towards a new and exciting result in the field: that every set of natural numbers that constitutes a positive proportion of all natural numbers contains the sum of any finite number of infinite sets.

算术组合学数学领域的一个中心主题是，在多大程度上仅凭大小就能保证加法结构。一个典型的问题沿着这些线是：对于哪些算术模式是它的情况下，任何足够大的数字集合是保证包含一个副本的模式？这项研究的目标是推动该领域一个新的令人兴奋的结果：构成所有自然数的正比例的每一组自然数都包含任何有限数量的无限集合的总和。

项目成果

Infinite Sumsets in Sets with Positive Density

• DOI: 10.1090/jams/1030
• 发表时间: 2022-06
• 作者: Bryna Kra;Joel Moreira;F. Richter;D. Robertson