论文标题
加强Freiman的3K-4定理
A strengthening of Freiman's 3k-4 theorem
论文作者
论文摘要
弗雷曼（Freiman）的3K-4定理以其通常的形式指出，如果a和b是大小为k的整数的子集，则具有较小的集合（尺寸接近2k），则它们非常接近算术进展。我们在本文中的目的是通过仅允许其中一组限制的可能的汇总来加强这一点。我们表明，如果a和b是大小k的整数的子集，因此对于B组的任何四元素子集X，AMSET A+X的大小的大小不超过2K，那么这已经意味着A和B非常接近算术进展。
In its usual form, Freiman's 3k-4 theorem states that if A and B are subsets of the integers of size k with small sumset (of size close to 2k) then they are very close to arithmetic progressions. Our aim in this paper is to strengthen this by allowing only a bounded number of possible summands from one of the sets. We show that if A and B are subsets of the integers of size k such that for any four-element subset X of B the sumset A+X has size not much more than 2k then already this implies that A and B are very close to arithmetic progressions.
