Partitioning 3-homogeneous latin bitrades |
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Authors: | Carlo Hämäläinen |
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Institution: | (1) Department of Mathematics, The University of Queensland, St. Lucia, 4072 Brisbane, Australia |
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Abstract: | A latin bitrade is a pair of partial latin squares that define 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 2] 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 in spherical, euclidean or hyperbolic space. Additionally, we show how latin bitrades are related to finite
representations of certain triangle groups.
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Keywords: | Latin square Latin bitrade Triangle group Tessellation |
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