Permutation Representation of 3 and 4-Homogenous Latin Bitrades

Abstract

Cavenagh, Donovan and Drápal (2005) gave a construction for 3-homogeneous latin bitrades which was proved by Cavenagh (2006) to give every 3-homogeneous latin bitrade. A corollary is that every 3-homogenous latin bitrade may be partitioned into three disjoint transversals. Using a permutation representation for latin bitrades developed by Drápal, we provide a shorter proof of these results, and then give a construction for a family of separated 4-homogeneous latin bitrades.