Defining sets for Latin squares given that they are based on groups
type: Item
instance of: scholarly article
title: Defining sets for Latin squares given that they are based on groups
zbMATH Open document ID: 1010.05013
DOI: 10.1016/S0195-6698(02)00115-4
author: David Bedford
author: Matthew Johnson
author: M. A. Ollis
published in: European Journal of Combinatorics
publication date: 2003-04-09T00:00:00Z
review text: A partial Latin square is an \(n\) by \(n\) array with elements from a set of size \(n\), such that no element appears more than once in any row or column. If a partial Latin square can be completed to a unique Latin square within the main class of a Latin square, denoted \(M(L)\), then it is said to be a defining set in \(M(L).\) The density of a defining set is the ratio of the size of the defining set and the number of entries in the Latin square, \(n^2\). The authors show that the density of the smallest defining sets in \(M(G)\), where \(G\) is a group, approaches \(0\) as \(n\) approaches infinity. Additionally, they disprove a conjecture of Keedwell by constructing a defining set of density \({7}\over{16}\) for each member of an infinite class of non-cyclic groups.
reviewed by: Steven T. Dougherty
Mathematics Subject Classification ID: 05B15
zbMATH DE Number: 1895805
zbMATH Keywords: latin squares
zbMATH Keywords: defining set
MaRDI profile type: Publication
cites work: Q4552244
cites work: Q3869366
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full work available at URL: s0195-6698(02)00115-4
OpenAlex ID: W2014044883
description: scientific article; zbMATH DE number 1895805