Geodesic
Embedding $3$-homogeneous latin trades into abelian $2$-groups
Commentationes Mathematicae Universitatis Carolinae, Tome 45 (2004) no. 2, pp. 191-212.

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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 $(L\setminus T)\cup T'$ 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.
Classification : 05B15, 20N05
Keywords: latin square; latin trade; abelian $2$-group 
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     title = {Embedding $3$-homogeneous latin trades into abelian $2$-groups},
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Cavenagh, Nicholas J. Embedding $3$-homogeneous latin trades into abelian $2$-groups. Commentationes Mathematicae Universitatis Carolinae, Tome 45 (2004) no. 2, pp. 191-212. http://geodesic.mathdoc.fr/item/CMUC_2004__45_2_a1/