Campus Units

Mathematics

Document Type

Article

Publication Version

Submitted Manuscript

Publication Date

6-30-2018

Journal or Book Title

arxiv

Abstract

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, Milicevic 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.

Comments

This is a manuscript made available through arxiv: https://arxiv.org/abs/1805.11278.

Copyright Owner

The Authors

Language

en

File Format

application/pdf

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