Perpendicular rectangular Latin arrays
type: Item
instance of: scholarly article
title: Perpendicular rectangular Latin arrays
zbMATH Open document ID: 1186.05032
author: Robert Brier
author: Darryn Bryant
published in: Graphs and Combinatorics
publication date: 2009-12-09T00:00:00Z
review text: A set \(\{A_1,A_2,\dots,A_t\}\) of rectangular arrays, each defined on a symbol set \(X\), is said to be \(t\)-perpendicular if each \(t\)-element subset of \(X\) occurs precisely once when the arrays are superimposed. The authors investigate the existence of sets of \(r \times s\) rectangular arrays which are row-Latin, column-Latin, and \(t\)-perpendicular. For example, they show that for all odd \(n\), there exists a pair of row- and column-Latin 2-perpendicular \(r \times s\) arrays with symbol set \(X\) of size \(n\) if and only if \(rs = \tbinom{n}{2}\) and \(r,s \leq n\). This is an interesting result in a paper that is nice to read.
reviewed by: Dan S. Archdeacon
Mathematics Subject Classification ID: 05B15
zbMATH DE Number: 5644625
zbMATH Keywords: perpendicular
zbMATH Keywords: arrays
zbMATH Keywords: orthogonal
zbMATH Keywords: Latin squares
MaRDI profile type: Publication
full work available at URL: s00373-008-0822-8
OpenAlex ID: W2071374461
cites work: A Combinatorial Problem on Abelian Groups
DOI: 10.1007/S00373-008-0822-8
description: scientific article; zbMATH DE number 5644625