# 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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We demonstrate how by using a reinforcement learning algorithm, the deep cross-entropy method, one can find explicit constructions and counterexamples to several open conjectures in extremalExpand
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Exact hyperplane covers for subsets of the hypercube