Exact hyperplane covers for subsets of the hypercube

被引：3
|
作者：
Aaronson, James [1 ]
Groenland, Carla [1 ]
Grzesik, Andrzej [2 ]
Johnston, Tom [1 ]
Kielak, Bartlomiej [2 ]
机构：
[1] Univ Oxford, Math Inst, Oxford OX2 6G, England
[2] Jagiellonian Univ, Fac Math & Comp Sci, Lojasiewicza, PL-30348 Krakow, Poland
来源：
DISCRETE MATHEMATICS | 2021年 / 344卷 / 09期
基金：
欧洲研究理事会;
关键词：
Hypercube; Intersection patterns; Hyperplanes; Exact covers;
D O I：
10.1016/j.disc.2021.112490
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Alon and Furedi (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. (c) 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
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