We prove that at least $\Omega(n^{0.51})$ hyperplanes are needed to slice all edges of the $n$-dimensional hypercube. We provide a couple of applications: lower bounds on the computational complexity of parity, and a lower bound on the cover number of the hypercube by skew hyperplanes.

中文翻译：

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切片超立方体并不容易

我们证明至少需要$ \ Omega（n ^ {0.51}）$个超平面来切片$ n $维超立方体的所有边缘。我们提供了两个应用程序：奇偶校验的计算复杂度的下限，以及倾斜超平面对超立方体的覆盖数的下限。