Constructions for regular-graph semi-Latin rectangles with block size two
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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.
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
Journal of Statistical Planning and Inference
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