论文标题
盖集问题：达到尺寸7
The cap set problem: Up to dimension 7
论文作者
论文摘要
S-CAP n-flat由一组S点给出，其中三个点在公共线上，在三个元素的n维仿射空间中。维度N中的CAP集问题是：最大s是什么，所以有一个s-cap n-flat？ 本系列文章中的前两篇论文考虑了限制的上限问题，包括5个。在本文中，这是该系列中的第三篇，我们考虑了第6和7：我们证明，每110 CAP 6-FLAT是112-CAP 6-FLAT是一个112-CAP 6-FLAT MINUS MINUS MINUS两个上限，并且没有289-Cap 7-flats。
An s-cap n-flat is given by a set of s points, no three of which are on a common line, in an n-dimensional affine space over the field of three elements. The cap set problem in dimension n is: what is the maximum s such that there is an s-cap n-flat? The first two papers in this series of articles considered the cap set problem in dimensions up to and including 5. In this paper, which is the third in the series, we consider dimensions 6 and 7: we prove that every 110-cap 6-flat is a 112-cap 6-flat minus two cap points, and that there are no 289-cap 7-flats.
