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dc.contributor.authorUto, Nseobong Peter
dc.contributor.authorBailey, R. A.
dc.identifier.citationUto , N P & Bailey , R A 2022 , ' Constructions for regular-graph semi-Latin rectangles with block size two ' , Journal of Statistical Planning and Inference , vol. 221 , pp. 81-89 .
dc.identifier.otherPURE: 278130183
dc.identifier.otherPURE UUID: b516944f-f7f1-42c5-8da5-7b9fd7890d48
dc.identifier.otherORCID: /0000-0002-8990-2099/work/110131560
dc.identifier.otherScopus: 85126571767
dc.identifier.otherWOS: 000795905400001
dc.description.abstractSemi-Latin rectangles are generalizations of Latin squares and semi-Latin squares. Although they are called rectangles, the number of rows and the number of columns are not necessarily distinct. There are k treatments in each cell (row-column intersection): these constitute a block. Each treatment of the design appears a definite number of times in each row and also a definite number of times in each column (these parameters also being not necessarily distinct). When k = 2, the design is said to have block size two. Regular- graph semi-Latin rectangles have the additional property that the treatment concurrences between any two pairs of distinct treatments differ by at most one. Constructions for semi-Latin rectangles of this class with k = 2 which have v treatments, v/2 rows and v columns, where v is even, are given in Bailey and Monod (2001). These give the smallest designs when v is even. Here we give constructions for smallest designs with k = 2 when v is odd. These are regular-graph semi-Latin rectangles where the numbers of rows, columns and treatments are identical. Then we extend the smallest designs in each case to obtain larger designs.
dc.relation.ispartofJournal of Statistical Planning and Inferenceen
dc.rightsCopyright © 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons. org/licenses/by-nc-nd/4.0/).en
dc.subjectRegular-graph semi-Latin rectangleen
dc.subjectBalanced tournament designen
dc.subjectTrojan squareen
dc.subjectUndirected terraceen
dc.subjectQA Mathematicsen
dc.titleConstructions for regular-graph semi-Latin rectangles with block size twoen
dc.typeJournal articleen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. Statisticsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.contributor.institutionUniversity of St Andrews. University of St Andrewsen
dc.description.statusPeer revieweden

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