划分3-齐次拉丁比特
Partitioning 3-homogeneous latin bitrades
摘要：
拉丁位交易$(T^{\diamond}, T^{\otimes})$是一对部分拉丁方，其定义了相同阶的两个任意拉丁方$L^{\diamond} \supseteq T^{\diamond}$和$L^{\diamond} \supseteq T^{\otimes}$之间的差。3齐次比特率$(T^{\diamond}, T^{\otimes})$在每行中具有三个条目，在每列中具有三个条目，并且每个符号在$T^{\diamond}$中出现三次。Cavenagh（2006）表明，任何3-齐次比特率都可以划分为三个横截。本文利用几何方法对Cavenagh的结果给出了一个独立的证明。在这样做的过程中，我们提供了一个研究bitrades的球面，欧几里得或双曲空间的镶嵌的框架。
英文摘要：
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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