论文标题
用两个填充的行和三个填充的列完成部分拉丁正方形
Completing partial Latin squares with two filled rows and three filled columns
论文作者
论文摘要
考虑一个部分拉丁广场$ p $，其中前两个行和前三列被完全填充，并且每个其他单元$ p $都是空的。已经猜想所有这些部分拉丁订单的平方至少$ 8 $都是可完整的。基于Kuhl和McGinn的技术，我们描述了一个框架，用于完成此类中的部分拉丁正方形。此外，我们使用我们的方法来证明该家族的所有部分拉丁正方形，在该家族中，非空行和列的相交形成一个带有三个不同符号的拉丁矩形，都是可以完成的。
Consider a partial Latin square $P$ where the first two rows and first three columns are completely filled, and every other cell of $P$ is empty. It has been conjectured that all such partial Latin squares of order at least $8$ are completable. Based on a technique by Kuhl and McGinn we describe a framework for completing partial Latin squares in this class. Moreover, we use our method for proving that all partial Latin squares from this family, where the intersection of the nonempty rows and columns form a Latin rectangle with three distinct symbols, is completable.
