Sub-latin squares and incomplete orthogonal arrays
نویسندگان
چکیده
منابع مشابه
A linear algebraic approach to orthogonal arrays and Latin squares
To study orthogonal arrays and signed orthogonal arrays, Ray-Chaudhuri and Singhi (1988 and 1994) considered some module spaces. Here, using a linear algebraic approach we define an inclusion matrix and find its rank. In the special case of Latin squares we show that there is a straightforward algorithm for generating a basis for this matrix using the so-called intercalates. We also extend this...
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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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A diagonal Latin square is a Latin square whose main diagonal and back diagonal are both transversals. In this paper we give some constructions of pairwise orthogonal diagonal Latin squares. As an application of such constructions we obtain some new infinite classes of pairwise orthogonal diagonal Latin squares which are useful in the study of pairwise orthogonal diagonal Latin squares.
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An incomplete self-orthogonal Latin square of order v with an empty subarray of order n, an ISOLS(v, n), can exist only if v ~ 3n + 1. This necessary condition is known to be sufficient apart from 2 known exceptions (v, n) = (6,1) and (8,2) plus 14 possible exceptions (v, n) with v = 3n + 2. In this paper, we construct eleven new ISOLS(3n + 2, n) reducing unknown n to 6, 8,10 only. This result ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1974
ISSN: 0097-3165
DOI: 10.1016/0097-3165(74)90069-7