Further Results on Quasi-Complete Latin Squares

Further results are given for quasi-complete latin squares. These are latin squares which have the property that every unordered pair of elements occurs next to each other exactly twice in rows and twice in columns. All possible squares with first row in natural order are considered up to size 6, wh...

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Bibliographic Details
Published in:Journal of the Royal Statistical Society. Series B, Methodological Methodological, 1981, Vol.43 (3), p.314-320
Main Author: Freeman, G. H.
Format: Article
Language:English
Subjects:
equality of occurrences of unordered pairs of neighbours in field trials
Experiment design
Experimentation
Genera
Latin squares
Natural order
nearest neighbour designs
Ordered pairs
pairs of quasi‐complete squares
quasi‐complete latin squares
Seed orchards
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Summary:Further results are given for quasi-complete latin squares. These are latin squares which have the property that every unordered pair of elements occurs next to each other exactly twice in rows and twice in columns. All possible squares with first row in natural order are considered up to size 6, while possible squares for sizes 7 to 9 are increasingly numerous so are considered progressively less exhaustively. Pairs of squares which together have equality of concurrences of ordered pairs of elements are also examined. The uses of quasi-complete squares for the practical design of field experiments requiring equality of occurrences of unordered pairs of neighbours are discussed.
ISSN:0035-9246
1369-7412
2517-6161
1467-9868
DOI:10.1111/j.2517-6161.1981.tb01677.x