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.

中文翻译：

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超立方体子集的精确超平面覆盖

Alon 和 Füredi (1993) 表明覆盖所需的超平面数量 ${\{0,1\}}^n\setminus \{0\}$不覆盖 0 是n。我们开始研究超立方体的其他子集的超立方体的这种精确的超平面覆盖。特别是，我们提供精确的覆盖解决方案${\{0,1\}}^n$而在一般情况下最多丢失四个点并给出渐近界限。几个有趣的问题悬而未决。