Minimal homogeneous latin trades Original Research Article

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 d-homogeneous latin trade is one which intersects each row, each column and each entry of the latin square either 0 or d times. In this paper we give a construction for minimal d-homogeneous latin trades of size dm, for every integer image, and image. We also improve this bound for small values of d. Our proof relies on the construction of cyclic sequences whose adjacent sums are distinct.