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Existence of sets of orthogonal Latin hyperrectangles

✍ Scribed by T. N. Eingorina

Book ID
112462578
Publisher
Springer US
Year
1969
Tongue
English
Weight
342 KB
Volume
12
Category
Article
ISSN
0033-8443

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πŸ“œ SIMILAR VOLUMES

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Maximal sets of s mutually orthogonal Latin squares of order v are constructed for infinitely many new pairs (s,v).

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We shall refer to a diagonal Latin square which is orthogonal to its (3, 2, 1)-conjugate and having its (3, 2, 1)-conjugate also a diagonal Latin square as a (3, 2, 1)-conjugate orthogonal diagonal Latin square, briefly CODLS. This article investigates the spectrum of CODLS and it is found that it c

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It is shown that for both v and n even, v > n > 0, there exists a pair of orthogonal latin squares of order v with an aligned subsquare of order n if and only if v ~> 3n, v ~ 6, n 4= 2, 6. This is the final case in showing that the above result is true for all v J: 6 and for all n ~ 2, 6. When n = 6