论文标题
超立方体子集的精确超平面盖
Exact hyperplane covers for subsets of the hypercube
论文作者
论文摘要
AlonandFüredi（1993）表明，覆盖$ \ {0,1 \}^n \ setMinus \ {0 \} $所需的超平面数量，而没有覆盖$ 0 $是$ n $。我们启动对超数据集的其他子集的超平方的精确超平面盖的研究。特别是，我们提供了确切的解决方案，用于覆盖$ \ {0,1 \}^n $，同时丢失了多达四个点并在一般情况下给出渐近界。几个有趣的问题将打开。
Alon and Füredi (1993) showed that the number of hyperplanes required to cover $\{0,1\}^n\setminus \{0\}$ without covering $0$ is $n$. We initiate the study of such exact hyperplane covers of the hypercube for other subsets of the hypercube. In particular, we provide exact solutions for covering $\{0,1\}^n$ while missing up to four points and give asymptotic bounds in the general case. Several interesting questions are left open.
