Embedding partial Latin squares in Latin squares with many mutually orthogonal mates
نویسندگان
چکیده
منابع مشابه
More mutually orthogonal Latin squares
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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Let J∗(v) be the set of all integers k such that there is a pair of Latin squares L and L′ with their own orthogonal mates on the same v-set, and with L and L′ having k cells in common. In this article we completely determine the set J∗(v) for integers v ≥ 24 and v = 1, 3, 4, 5, 8, 9. For v = 7 and 10 ≤ v ≤ 23, there are only a few cases left undecided for the set J∗(v).
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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: 2020
ISSN: 0012-365X
DOI: 10.1016/j.disc.2020.111835