Permutation Representation of 3 and 4-Homogenous Latin Bitrades

Issue title: Workshop on Combinatorial Algorithms

Article type: Research Article

Authors: Lefevre, James G. | Donovan, Diane | Drápal, Aleš

Affiliations: Centre for Discrete Mathematics and Computing, University of Queensland St Lucia 4072 Australia. E-mails: {jgl,dmd}@maths.uq.edu.au | Department of Mathematics, Charles University, 186 75 Prague, Czech Republic. E-mail: drapal@karlin.mff.cuni.cz

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.

Keywords: Latin trade, latin bitrade, homogeneous

Journal: Fundamenta Informaticae, vol. 84, no. 1, pp. 99-110, 2008