Geodesic
A uniqueness result for $3$-homogeneous latin trades
Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 2, pp. 337-358.

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A latin trade is a subset of a latin square which may be replaced with a disjoint mate to obtain a new latin square. A $k$-homogeneous latin trade is one which intersects each row, each column and each entry of the latin square either $0$ or $k$ times. In this paper, we show that a construction given by Cavenagh, Donovan and Drápal for $3$-homogeneous latin trades in fact classifies every minimal $3$-homogeneous latin trade. We in turn classify all $3$-homogeneous latin trades. A corollary is that any $3$-homogeneous latin trade may be partitioned into three, disjoint, partial transversals.
Classification : 05B15
Keywords: latin square; latin trade; critical set 
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     title = {A uniqueness result for $3$-homogeneous latin trades},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {337--358},
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Cavenagh, Nicholas J. A uniqueness result for $3$-homogeneous latin trades. Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 2, pp. 337-358. http://geodesic.mathdoc.fr/item/CMUC_2006__47_2_a10/