Embedding 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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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.
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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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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: Proceedings of the American Mathematical Society
سال: 1976
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1976-0409227-2