A polynomial embedding of pairs of orthogonal partial Latin squares
نویسندگان
چکیده
منابع مشابه
Nearly 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...
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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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In this thesis, the problem of completing partial latin squares is examined. In particular, the completion problem for three primary classes of partial latin squares is investigated. First, the theorem of Marshall Hall regarding completions of latin rectangles is discussed. Secondly, a proof of Evans’ conjecture is presented, which deals with partial latin squares of order n containing at most ...
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We introduce the notion of premature partial latin squares; these cannot be completed, but if any of the entries is deleted, a completion is possible. We study their spectrum, i.e., the set of integers t such that there exists a premature partial latin square of order n with exactly t nonempty cells.
متن کاملOn Non-Polynomial Latin Squares
A Latin square L = L(`ij) over the set S = {0, 1, . . . , n − 1} is called totally non-polynomial over Zn iff 1. there are no polynomials Ui(y) ∈ Zn[y] such that Ui(j) = `ij for all i, j ∈ Zn; 2. there are no polynomials Vj(x) ∈ Zn[x] such that Vj(i) = `ij for all i, j ∈ Zn. In the presented paper we describe four possible constructions of such Latin squares which might be of particular interes...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2014
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2014.04.003