论文标题
Varikon框的代数结构
Algebraic Structure of the Varikon Box
论文作者
论文摘要
15个插头是一个经过良好研究的置换拼图。本文探讨了15个插头的三维变体的组结构，称为Varikon盒子，其目的是提供一种启发式，该启发式将有助于人类解决，同时最大程度地减少动作数量。首先，我们通过一个奇偶校验证明了拼图的配置。我们根据运动的三个维度来定义生成集，该集合会生成一个作用于拼图配置的组，并探索该组的结构。最后，我们通过将对称组的元素写为生成集来展示一种用于解决难题的启发式，并计算每个拼图配置的最短单词。
The 15-Puzzle is a well studied permutation puzzle. This paper explores the group structure of a three-dimensional variant of the 15-Puzzle known as the Varikon Box, with the goal of providing a heuristic that would help a human solve it while minimizing the number of moves. First, we show by a parity argument which configurations of the puzzle are reachable. We define a generating set based on the three dimensions of movement, which generates a group that acts on the puzzle configurations, and we explore the structure of this group. Finally, we show a heuristic for solving the puzzle by writing an element of the symmetry group as a word in terms of a generating set, and we compute the shortest possible word for each puzzle configuration.
