Slicing the hypercube is not easy

02/10/2021

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by   Gal Yehuda, et al.

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We prove that at least Ω(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.