Mathematics – Combinatorics
Scientific paper
2007-10-04
Mathematics
Combinatorics
13 pages, 11 figures, fixed the figures. Geometriae Dedicata, Accepted: 13 February 2008, Published online: 5 March 2008
Scientific paper
10.1007/s10711-008-9242-4
A latin bitrade $(T^{\diamond}, T^{\otimes})$ is a pair of partial latin squares 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 $(T^{\diamond}, T^{\otimes})$ has three entries in each row, three entries in each column, and each symbol appears three times in $T^{\diamond}$. Cavenagh (2006) showed that any 3-homogeneous bitrade may be partitioned into three transversals. In this paper we provide an independent proof of Cavenagh's result using geometric methods. In doing so we provide a framework for studying bitrades as tessellations of spherical, euclidean or hyperbolic space.
No associations
LandOfFree
Partitioning 3-homogeneous latin bitrades does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Partitioning 3-homogeneous latin bitrades, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Partitioning 3-homogeneous latin bitrades will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-563123