Further results on incomplete (3,2,1)- conjugate orthogonal idempotent Latin squares
نویسندگان
چکیده
منابع مشابه
Further Results on the Construction of Mutually Orthogonal Latin Squares and the Falsity of Euler's Conjecture
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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Denote by Fin(v) the set of all integer pairs (t, s) for which there exist three Latin squares of order v on the same set having fine structure (t, s). The set Fin(v) with v ≥ 2 and v = 5, 6, 7, 8 is determined in [2]. In the present article the set Fin(8) is finally determined. Some results on Fin(v) with 5 ≤ v ≤ 7 are also updated.
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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...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1990
ISSN: 0012-365X
DOI: 10.1016/0012-365x(90)90267-l