Existence of orthogonal latin squares with aligned subsquares
نویسندگان
چکیده
منابع مشابه
Most Latin Squares Have Many Subsquares
A k_n Latin rectangle is a k_n matrix of entries from [1, 2, ..., n] such that no symbol occurs twice in any row or column. An intercalate is a 2_2 Latin subrectangle. Let N(R) be the number of intercalates in R, a randomly chosen k_n Latin rectangle. We obtain a number of results about the distribution of N(R) including its asymptotic expectation and a bound on the probability that N(R)=0. For...
متن کاملThe Existence of Latin Squares without Orthogonal Mates
A latin square is a bachelor square if it does not possess an orthogonal mate; equivalently, it does not have a decomposition into disjoint transversals. We define a latin square to be a confirmed bachelor square if it contains an entry through which there is no transversal. We prove the existence of confirmed bachelor squares for all orders greater than three. This resolves the existence quest...
متن کاملOn 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 ...
متن کاملNearly Orthogonal Latin Squares
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 کاملMore 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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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1986
ISSN: 0012-365X
DOI: 10.1016/0012-365x(86)90070-1