# Exact hyperplane covers for subsets of the hypercube

@article{Aaronson2021ExactHC, title={Exact hyperplane covers for subsets of the hypercube}, author={James Aaronson and C. Groenland and A. Grzesik and Tom Johnston and Bartlomiej Kielak}, journal={Discret. Math.}, year={2021}, volume={344}, pages={112490} }

Alon and Furedi (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.

#### 2 Citations

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Alon and Füredi (European J. Combin., 1993) proved that any family of hyperplanes that covers every point of the Boolean cube {0, 1}n except one must contain at least n hyperplanes. We obtain two… Expand

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Exact hyperplane covers for subsets of the hypercube