Exact hyperplane covers for subsets of the hypercube

James Aaronson, Carla Groenland, Andrzej Grzesik, Tom Johnston, Bartłomiej Kielak

Research output: Contribution to journalArticleAcademicpeer-review


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.

Original languageEnglish
Article number112490
Pages (from-to)1-7
JournalDiscrete Mathematics
Issue number9
Publication statusPublished - Sept 2021


  • Exact covers
  • Hypercube
  • Hyperplanes
  • Intersection patterns


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