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Exact hyperplane covers for subsets of the hypercube
- Publication Year :
- 2020
-
Abstract
- Alon and F\"{u}redi (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.<br />Comment: Small fixes and updated code
- Subjects :
- Mathematics - Combinatorics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2010.00315
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.disc.2021.112490