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Constructions for regular-graph semi-Latin rectangles with block size two
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dc.contributor.author | Uto, Nseobong Peter | |
dc.contributor.author | Bailey, R. A. | |
dc.date.accessioned | 2022-07-07T14:30:04Z | |
dc.date.available | 2022-07-07T14:30:04Z | |
dc.date.issued | 2022-12 | |
dc.identifier | 278130183 | |
dc.identifier | b516944f-f7f1-42c5-8da5-7b9fd7890d48 | |
dc.identifier | 85126571767 | |
dc.identifier | 000795905400001 | |
dc.identifier.citation | Uto , 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 . https://doi.org/10.1016/j.jspi.2022.02.007 | en |
dc.identifier.issn | 0378-3758 | |
dc.identifier.other | ORCID: /0000-0002-8990-2099/work/110131560 | |
dc.identifier.uri | https://hdl.handle.net/10023/25625 | |
dc.description.abstract | Semi-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.format.extent | 425297 | |
dc.language.iso | eng | |
dc.relation.ispartof | Journal of Statistical Planning and Inference | en |
dc.subject | Regular-graph semi-Latin rectangle | en |
dc.subject | Starter | en |
dc.subject | Bi-starter | en |
dc.subject | Balanced tournament design | en |
dc.subject | Trojan square | en |
dc.subject | Undirected terrace | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject.lcc | QA | en |
dc.title | Constructions for regular-graph semi-Latin rectangles with block size two | en |
dc.type | Journal article | en |
dc.contributor.institution | University of St Andrews. Statistics | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.contributor.institution | University of St Andrews. University of St Andrews | en |
dc.identifier.doi | https://doi.org/10.1016/j.jspi.2022.02.007 | |
dc.description.status | Peer reviewed | en |
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