Abstract Prior to using computational tools that find the autotopism group of a partial Latin rectangle (its stabilizer group under row, column and symbol permutations), it is beneficial to find partitions of the rows, columns and symbols that are invariant under autotopisms and are as fine as possible. We look at the lattices formed by these partitions and introduce two invariant refining maps on these lattices. The first map generalizes the strong entry invariant in a previous work. The second map utilizes some bipartite graphs, introduced here, whose structure is determined by pairs of rows (or columns, or symbols). Experimental results indicate that in most cases (ordinarily 99%+), the combined use of these invariants gives the theoretical best partition of the rows, columns and symbols, outperforms the strong entry invariant, which only gives the theoretical best partitions in roughly 80% of the cases.

中文翻译：

---

用于计算部分拉丁矩形的自拓扑群的精炼不变量

摘要 在使用计算工具寻找部分拉丁矩形（其行、列和符号排列下的稳定器组）的自拓扑群之前，有利于找到在自拓扑下不变的行、列和符号的分区，如尽可能好。我们查看由这些分区形成的格子，并在这些格子上引入两个不变的细化图。第一张图概括了先前工作中的强入口不变量。第二张图利用了这里介绍的一些二部图，其结构由成对的行（或列或符号）决定。实验结果表明，在大多数情况下（通常为 99%+），这些不变量的组合使用给出了行、列和符号的理论上的最佳分区，优于强入口不变量，