On partitions of discrete boxes
type: Item
instance of: scholarly article
title: On partitions of discrete boxes
zbMATH Open document ID: 1034.52021
DOI: 10.1016/S0012-365X(02)00428-4
author: Noga Alon
author: Tom Bohman
author: Ron Holzman
author: Daniel J. Kleitman
published in: Discrete Mathematics
publication date: 2002-12-02T00:00:00Z
review text: A set of the form \(A=A_1 \times A_2 \times \dots \times A_n\), where \(A_1, A_2, \dots, A_n\) are finite sets with \(| A_i| \geq 2\), is called an \(n\)-dimensional discrete box. A set of the form \(B=B_1 \times B_2 \times \dots \times B_n\), where \(B_i \subseteq A_i\), \(i=1, \dots ,n\), is a sub-box of \(A\). Such a set \(B\) is said to be nontrivial if \(\emptyset \not= B_i \not= A_i\) for every \(i\). It is proved that any partition of an \(n\)-dimensional discrete box into nontrivial sub-boxes must consist of at least \(2^n\) sub-boxes. Furthermore, some extensions of this result are considered.
reviewed by: Arnfried Kemnitz
Mathematics Subject Classification ID: 52C99
Mathematics Subject Classification ID: 05A18
zbMATH DE Number: 1838991
zbMATH Keywords: partition
zbMATH Keywords: discrete box
zbMATH Keywords: sub-box
Wikidata QID: Q101165570
MaRDI profile type: Publication
full work available at URL: s0012-365x(02)00428-4
OpenAlex ID: W1981805744
description: scientific article; zbMATH DE number 1838991