幻数独变体的套图和极小完全对称群
Nest graphs and minimal complete symmetry groups for magic Sudoku variants
摘要：
一个数独的对称群是完备的，如果它的作用将数独棋盘的集合分成所有可能的轨道，并且如果没有更小的群会这样做，那么它是最小的。在此之前，对于4 x 4的数独变体Shidoku，作者使用类似的对称群将Shidoku板的集合划分为所谓的“巢”，然后使用物理和重新标记对称之间的相互作用来找到某些既完整又最小的子群。在本文中，这些相同的技术被应用到找到一个最小的完整对称群的模块化魔术数独的变化，以及为另一个数独的变化称为半魔术数独。最后，本文通过一个简单的计算得出了一个不明显的事实，即完整的数独对称群实际上已经是最小的和完整的。
英文摘要：
A symmetry group for Sudoku is complete if its action partitions the set of Sudoku boards into all possible orbits, and minimal if no group of smaller size would do the same. Previously, for a 4 x 4 Sudoku variation known as Shidoku, the authors used an analogous symmetry group to partition the set of Shidoku boards into so-called "nests" and then use the interplay between the physical and relabeling symmetries to find certain subgroups that were both complete and minimal. In this paper these same techniques are applied to find a minimal complete symmetry group for the modular magic Sudoku variation, as well as for another Sudoku variation called semi-magic Sudoku. The paper concludes with a simple computation which leads to the non-obvious fact that the full Sudoku symmetry group is, in fact, already minimal and complete.
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