4 research outputs found
Partitioning 3-homogeneous latin bitrades
A latin bitrade is a pair of partial latin
squares which defines the difference between two arbitrary latin squares
and
of the same order. A 3-homogeneous bitrade has
three entries in each row, three entries in each column, and each symbol
appears three times in . 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.Comment: 13 pages, 11 figures, fixed the figures. Geometriae Dedicata,
Accepted: 13 February 2008, Published online: 5 March 200