Exact hyperplane covers for subsets of the hypercube
James Aaronson (University of Oxford)
Carla Groenland (University of Oxford)
Andrzej Grzesik (Jagiellonian University)
Tom Johnston (University of Oxford)
Bartłomiej Kielak (Jagiellonian University)
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Abstract
Alon and Füredi (1993) showed that the number of hyperplanes required to cover {0,1}n∖{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.
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