Partition problems in high dimensional boxes

Alon, Bohman, Holzman and Kleitman proved that any partition of a d-dimensional discrete box into proper sub-boxes must consist of at least 2d sub-boxes. Recently, Leader, Milićević and Tan considered the question of how many odd-sized proper boxes are needed to partition a d-dimensional box of odd...

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Bibliographic Details
Published inJournal of combinatorial theory. Series A Vol. 166; pp. 315 - 336
Main Authors Bucic, Matija, Lidický, Bernard, Long, Jason, Wagner, Adam Zsolt
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.08.2019
Subjects
High dimensional boxes
Linear programming
Partition problems
High dimensional boxes
Linear programming
Partition problems
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ISSN0097-3165
1096-0899
DOI10.1016/j.jcta.2019.02.011

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Summary:Alon, Bohman, Holzman and Kleitman proved that any partition of a d-dimensional discrete box into proper sub-boxes must consist of at least 2d sub-boxes. Recently, Leader, Milićević and Tan considered the question of how many odd-sized proper boxes are needed to partition a d-dimensional box of odd size, and they asked whether the trivial construction consisting of 3d boxes is best possible. We show that approximately 2.93d boxes are enough, and consider some natural generalisations.
ISSN:0097-3165
1096-0899
DOI:10.1016/j.jcta.2019.02.011