Six pairwise orthogonal latin squares of order 69
نویسندگان
چکیده
منابع مشابه
The Search for Pseudo Orthogonal Latin Squares of Order Six
We report on the complete computer search for a strongly regular graph with parameters (36,15,6,6) and chromatic number six. The result is that no such graph exists.
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A diagonal Latin square is a Latin square whose main diagonal and back diagonal are both transversals. Let dr be the least integer such that for all n > dr there exist r pairwise orthogonal diagonal Latin squares of order n. In a previous paper Wallis and Zhu gave several bounds on the dr. In this paper we shall present some constructions of pairwise orthogonal diagonal Latin squares and conseq...
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A Latin square of order s is an s by s array L of the symbols { 1,2,..., s}, such that each symbol occurs once in each row and column of L. Two Latin squares L and M of order s are orthogonal if their superposition yields all s2 possible ordered pairs (i,j), 1 < i, j < s. It was conjectured by Euler, and proved by Tarry [4] that there do not exist a pair of orthogonal Latin squares of order six...
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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: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
سال: 1984
ISSN: 0263-6115
DOI: 10.1017/s1446788700021698