4 research outputs found

    Partitioning 3-homogeneous latin bitrades

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    A latin bitrade (T⋄,T⊗)(T^{\diamond}, T^{\otimes}) is a pair of partial latin squares which defines the difference between two arbitrary latin squares L⋄⊇T⋄L^{\diamond} \supseteq T^{\diamond} and L⋄⊇T⊗L^{\diamond} \supseteq T^{\otimes} of the same order. A 3-homogeneous bitrade (T⋄,T⊗)(T^{\diamond}, T^{\otimes}) has three entries in each row, three entries in each column, and each symbol appears three times in T⋄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.Comment: 13 pages, 11 figures, fixed the figures. Geometriae Dedicata, Accepted: 13 February 2008, Published online: 5 March 200

    On which groups can arise as the canonical group of a spherical latin bitrade

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