Finite and infinite arithmetic progressions in sumsets

• 成果类型: Article
• 署名作者: Szemeredi, E.; Vu, V. H.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2006.163.1
• 发表日期: 2006
• 页码: 1-35
• 关键词: sum-free sets; distinct terms; Integers; REPRESENTATION

摘要

We prove that if A is a subset of at least cn(1/2) elements of {1,..., n}, where c is a sufficiently large constant, then the collection of subset sums of A contains an arithmetic progression of length n. As an application, we confirm a long standing conjecture of Erdos and Folkman on complete sequences.