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Slicing the hypercube is not easy
Published 10 Feb 2021 in math.CO, cs.AI, and cs.CC | (2102.05536v2)
Abstract: 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.
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