标题： 关于具有不相交子方的拉丁方的新结果：利用有理轮廓方的拉丁方 显示英文标题

标题： Further results on latin squares with disjoint subsquares using rational outline squares

摘要： 本文我们研究了具有互不相交子方阵集合的拉丁方问题。我们提出了关于子方阵大小的一个新的必要条件，该条件综合并扩展了已知的条件。我们给出了当所有子方阵除两个之外都同尺寸时的一种构造方法，在此情况下该条件是充分的。我们利用对称有理轮廓方阵得到了这些结果，并且额外提供了该理论的若干新结果和扩展。 显示英文摘要

摘要： In this paper we consider the problem of finding latin squares with sets of pairwise disjoint subsquares. We develop a new necessary condition on the sizes of the subsquares which incorporates and extends the known conditions. We provide a construction for the case where all but two of the subsquares are the same size, and in this case the condition is sufficient. We obtain these results using symmetric rational outline squares, and additionally provide several new results and extensions to this theory.