Nicholas J. Cavenagh
Embedding $3$-homogeneous latin trades into abelian $2$-groups

Comment.Math.Univ.Carolinae 45,2 (2004) 191-212.

Abstract: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.

Keywords: latin square, latin trade, abelian $2$-group
AMS Subject Classification: 05B15, 20N05