Magic rectangles and modular magic rectangles
type: Item
instance of: scholarly article
title: Magic rectangles and modular magic rectangles
zbMATH Open document ID: 0851.05031
DOI: 10.1016/0378-3758(95)00081-X
author: Anthony B. Evans
published in: Journal of Statistical Planning and Inference
publication date: 1996-11-21T00:00:00Z
review text: A magic \(( m, n)\) rectangle is an \(m\times n\) matrix with entries \(1,\dots, mn\) for which all the row sums are the same and all the column sums are the same. A modular magic \((m, n)\) rectangle is an \(m\times n\) matrix with entries \(1,\dots, mn\) for which all the row sums are congruent modulo \(mn\) and all the column sums are congruent modulo \(mn\). It is shown that the existence criteria for modular magic rectangles are virtually the same as for magic rectangles. Two classes of modular magic rectangles are studied: pseudomagic and complete magic rectangles. Three open problems are mentioned.
Mathematics Subject Classification ID: 05B15
Mathematics Subject Classification ID: 05B99
zbMATH DE Number: 906655
zbMATH Keywords: modular magic rectangles
zbMATH Keywords: magic rectangles
reviewed by: Giacomo Bonanno
MaRDI profile type: Publication
cites work: Q5784990
cites work: Balanced magic rectangles
cites work: Q4769064
cites work: Existence of magic rectangles
full work available at URL: 0378-3758(95)00081-x
OpenAlex ID: W2019699708
description: scientific article; zbMATH DE number 906655