A uniqueness result for $3$-homogeneous latin trades

Nicholas J. Cavenagh

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Embedding $3$ -homogeneous latin trades into abelian $2$ -groups

Nicholas J. Cavenagh (2004)

Commentationes Mathematicae Universitatis Carolinae

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Let $T$ be a partial latin square and $L$ be a latin square with $T \subseteq L$ . We say that $T$ is a latin trade if there exists a partial latin square $T^{'}$ with $T^{'} \cap T = \emptyset$ such that $(L ∖ T) \cup T^{'}$ is a latin square. A $k$ -homogeneous latin trade is one which intersects each row, each column and each entry either $0$ or $k$ times. In this paper, we show the existence of $3$ -homogeneous latin trades in abelian $2$ -groups.