Partitioning 3-homogeneous latin bitrades

Details Partitioning 3-homogeneous latin bitrades Partitioning 3-homogeneous latin bitrades

2007-10-04

arxiv.org/abs/0710.0938v3

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.

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