An n to 2n embedding of incomplete idempotent latin squares for small values of n
نویسندگان
چکیده
منابع مشابه
A Solution to the Embedding Problem for Partial Idempotent Latin Squares
A partial latin square on t symbols <rl5..., ut of side n is an n x n matrix, each of the cells of which may be empty or may be occupied by. one of the symbols ol,..., at, and which satisfies the rule that no symbol occurs more than once in any row or more than once in any column. An incomplete latin square on t symbols of side n is a partial latin square in which there are no empty cells; it i...
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It is known that t mutually orthogonal latin squares of order n generate a b t 2c-error correcting code with n codewords. In this paper we consider latin squares of order n made up of elements taken from Zn. In this situation we consider when this code is linear. We present neccessary and sufficient conditions on the latin squares and obtain a method of constructing a maximal family of mutually...
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We use the concept of an availability matrix, introduced in Euler [7], to describe the family of all minimal incomplete 3 × n latin rectangles that are not completable. We also present a complete description of minimal incomplete such latin squares of order 4.
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Some Constructions of Non-Commutative Latin Squares of Order n
Let n be an integer. We show the existence of at least three non-isomorphic non-commutative Latin squares of order n which are embeddable in groups when n ≥ 5 is odd. By using a similar construction for the case when n ≥ 4 is even, we show that certain non-commutative Latin squares of order n are not embeddable in groups. Keywords—group, Latin square, embedding.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2000
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(99)00134-x