Generalizations of Bose's equivalence between complete sets of mutually orthogonal Latin squares and affine planes
نویسندگان
چکیده
منابع مشابه
Maximal sets of mutually orthogonal Latin squares
Maximal sets of s mutually orthogonal Latin squares of order v are constructed for in nitely many new pairs (s; v). c © 1999 Published by Elsevier Science B.V. All rights reserved
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We present a general technique for obtaining permutation polynomials over a finite field from permutations of a subfield. By applying this technique to the simplest classes of permutation polynomials on the subfield, we obtain several new families of permutation polynomials. Some of these have the additional property that both f(x) and f(x) + x induce permutations of the field, which has combin...
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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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We show how to produce algebraically a complete orthogonal set of Latin squares from a left quasifield and how to generate algebraically a maximal set of self-orthogonal Latin squares from a left nearfield. For a left Veblen-Wedderburn system, we establish the algebraic relationships between the standard projective plane construction of a complete set of Latin squares, our projective plane cons...
متن کاملOn the Structure and Classification of SOMAs: Generalizations of Mutually Orthogonal Latin Squares
Let k ≥ 0 and n ≥ 2 be integers. A SOMA, or more specifically a SOMA(k, n), is an n×n array A, whose entries are k-subsets of a kn-set Ω, such that each element of Ω occurs exactly once in each row and exactly once in each column of A, and no 2-subset of Ω is contained in more than one entry of A. A SOMA(k, n) can be constructed by superposing k mutually orthogonal Latin squares of order n with...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1992
ISSN: 0097-3165
DOI: 10.1016/0097-3165(92)90050-5