A latin bitrade is a pair of partial latin squares which are disjoint, occupy the same set of non-
empty cells, and whose corresponding rows and columns contain the same sets of symbols …

Cycle switches are the simplest changes which can be used to alter latin squares, and as
such have found many applications in the generation of latin squares. They also provide the …

Let T be a partial latin square and L be a latin square with T⊆ L. We say that T is a latin
trade if there exists a partial latin square T′ with T′∩ T=∅ such that (L⧹ T)∪ T′ is a latin …

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 …

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 …

To study orthogonal arrays and signed orthogonal arrays, Ray-Chaudhuri and Singhi (1988
and 1994) considered some module spaces. Here, using a linear algebraic approach we …

This thesis consists of the four papers listed below and a survey of the research area. I Lina
J. Andrén: Avoiding (m, m, m)-arrays of order n= 2k II Lina J. Andrén: Avoidability of random …

By simulating an ergodic Markov chain whose stationary distribution is uniform over the
space of nxn Latin squares, Mark T. Jacobson and Peter Matthews [4], have discussed …

A Steiner 2-(v, 3) trade is a pair (T1, T2) of disjoint partial Steiner triple systems, each on the
same set of v points, such that each pair of points occurs in T1 if and only if it occurs in T2. A …

In this paper, using some linear algebraic methods, we show that every latin tade can be
produced by intercalates (ie latin trades of volume 4). A similar result is true for 4-cycle …