# Partitioning 3-homogeneous latin bitrades - Mathematics > Combinatorics

Abstract: A latin bitrade $T^{\diamond}, T^{\otimes}$ is a pair of partial latinsquares which defines the difference between two arbitrary latin squares$L^{\diamond} \supseteq T^{\diamond}$ and $L^{\diamond} \supseteq T^{\otimes}$of the same order. A 3-homogeneous bitrade $T^{\diamond}, T^{\otimes}$ hasthree entries in each row, three entries in each column, and each symbolappears three times in $T^{\diamond}$. Cavenagh 2006 showed that any3-homogeneous bitrade may be partitioned into three transversals. In this paperwe provide an independent proof of Cavenagh-s result using geometric methods.In doing so we provide a framework for studying bitrades as tessellations ofspherical, euclidean or hyperbolic space.

Author: Carlo Hamalainen

Source: https://arxiv.org/