Latin trades on three or four rows

4-homogeneous Latin Trades

Minimal homogeneous latin trades

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 d 3, and m 1.75d2 + 3. We also improve this b...

3-Homogeneous latin trades

Latin trades and simplicial complexes

In this note we introduce the concept of the trade space of a latin square. Computations using Sage and the GAP package Simplicial Homology are presented.

On the intersection of three or four transversals of the back circulant latin squares

Cavenagh and Wanless [Discrete Appl. Math. 158 no. 2 (2010), 136–146] determined the possible intersection of any two transversals of the back circulant latin square Bn, and used the result to completely determine the spectrum for 2-way k-homogeneous latin trades. We generalize this problem to the intersection of μ transversals of Bn such that the transversals intersect stably (that is, the int...