论文标题
盖子组的新下限
New Lower Bounds for Cap Sets
论文作者
论文摘要
盖子集是$ \ mathbb {f} _3^n $的子集，而没有解决方案的$ x+y+z = 0 $，而不是$ x = y = y = z $。在本文中，我们在最大盖集的大小上提供了一个新的下限。在Edel的构造构建基础上，我们使用改进的计算方法和新的理论思想，以表明，对于足够大的$ n $，总有$ \ Mathbb {f} _3^n $大小至少$ 2.218^n $中的上限。
A cap set is a subset of $\mathbb{F}_3^n$ with no solutions to $x+y+z=0$ other than when $x=y=z$. In this paper, we provide a new lower bound on the size of a maximal cap set. Building on a construction of Edel, we use improved computational methods and new theoretical ideas to show that, for large enough $n$, there is always a cap set in $\mathbb{F}_3^n$ of size at least $2.218^n$.
