A further construction of double diagonal orthogonal latin squares
نویسندگان
چکیده
منابع مشابه
On the existence of self-orthogonal diagonal Latin squares
A diagonal Latin square is a Latin square whose main diagonal and back diagonal are both transversals. A Latin square is self-orthogonal if it is orthogonal to its transpose. In an earlier paper Danhof, Phillips and Wallis considered the question of the existence of self-orthogonal diagonal Latin squares of order 10. In this paper we shall present some constructions of self-orthogonal diagonal ...
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A diagonal Latin square is a Latin square whose main diagonal and back diagonal are both transversals. Let dr be the least integer such that for all n > dr there exist r pairwise orthogonal diagonal Latin squares of order n. In a previous paper Wallis and Zhu gave several bounds on the dr. In this paper we shall present some constructions of pairwise orthogonal diagonal Latin squares and conseq...
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MacNeish's conjecture was disproved by Parker (12) who showed that in certain cases N(v) > n(v) by proving that if there exists a balanced incomplete block (BIB) design with v treatments, A = 1, and block size k which is a prime power then N(v) > k — 2, and that this result can be improved to N(v) > k — 1, when the design is symmetric and cyclic. Parker's result though it did not disprove Euler...
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A Latin square of order n is an n by n array in which every row and column is a permutation of a set N of n elements. Let L = [li,j ] and M = [mi,j ] be two Latin squares of even order n, based on the same N -set. Define the superposition of L onto M to be the n by n array A = (li,j ,mi,j). When n is even, L and M are said to be nearly orthogonal if the superposition of L onto M has every order...
متن کاملStrongly symmetric self-orthogonal diagonal Latin squares and Yang Hui type magic squares
Keywords: Self-orthogonal Latin square Strongly symmetric Magic square Yang Hui type a b s t r a c t In this paper, a strongly symmetric self-orthogonal diagonal Latin square of order n with a special property (* SSSODLS(n)) is introduced. It is proved that a * SSSODLS(n) exists if and only if n ≡ 0 (mod 4) and n ̸ = 4. As an application, it is shown that there exists a Yang Hui type magic squar...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1974
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(74)80023-3