On the spectrum of r-self-orthogonal Latin squares
نویسندگان
چکیده
منابع مشابه
On the spectrum of r-self-orthogonal Latin squares
Two Latin squares of order n are r-orthogonal if their superposition produces exactly r distinct ordered pairs. If the second square is the transpose of the 3rst one, we say that the 3rst square is r-self-orthogonal, denoted by r-SOLS(n). It has been proved that the necessary condition for the existence of an r-SOLS(n) is n6 r6 n and r ∈ {n + 1; n − 1}. Zhu and Zhang conjectured that there is a...
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two latin squares of order $n$ are orthogonal if in their superposition, each of the$n^{2}$ ordered pairs of symbols occurs exactly once. colbourn, zhang and zhu, in a seriesof papers, determined the integers $r$ for which there exist a pair of latin squares oforder $n$ having exactly $r$ different ordered pairs in their superposition. dukes andhowell defined the same problem for latin squares ...
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Two Latin squares of order n are orthogonal if in their superposition, each of the n ordered pairs of symbols occurs exactly once. Colbourn, Zhang and Zhu, in a series of papers, determined the integers r for which there exist a pair of Latin squares of order n having exactly r different ordered pairs in their superposition. Dukes and Howell defined the same problem for Latin squares of differe...
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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 ...
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 ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2004
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(03)00288-7