On Embedding and Enumeration of Orthogonal Latin Squares
نویسندگان
چکیده
منابع مشابه
Enumeration of self-orthogonal Latin squares
The enumeration of self-orthogonal Latin squares (SOLS) of a given order seems to be an open problem in the literature on combinatorial designs. The existence of at least one SOLS is guaranteed for any order except 2, 3 and 6, but it is not known how many of these squares of a given order exist. In this talk we present enumeration tables of unequal SOLS, idempotent SOLS, isomorphism classes of ...
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The numbers of distinct self-orthogonal Latin squares (SOLS) and idempotent SOLS have been enumerated for orders up to and including 9. The isomorphism classes of idempotent SOLS have also been enumerated for these orders. However, the enumeration of the isomorphism classes of non-idempotent SOLS is still an open problem. By utilising the automorphism groups of class representatives from the al...
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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 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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Orthogonal latin squares of Sudoku type Hans-Dietrich Gronau Universität Rostock, Inst. für Mathematik 18051 Rostock, Germany We present results on the existence of orthogonal latin squares and latin rectangles of Sudoku type.
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ژورنال
عنوان ژورنال: The Annals of Mathematical Statistics
سال: 1971
ISSN: 0003-4851
DOI: 10.1214/aoms/1177693401