论文标题
滑动块拼图有一个扭曲：在Segerman的15+4个难题上
Sliding Block Puzzles with a Twist: On Segerman's 15+4 Puzzle
论文作者
论文摘要
塞格曼（Segerman）的15+4个拼图是经典15 puzzle的铰链版本，其中瓷砖在滑动时旋转。 1974年，威尔逊（Wilson）将解决方案组归类为滑动障碍。我们将威尔逊的结果推广到诸如瓷砖可以旋转的15+4个拼图之类的难题，而解决方案集则是广义对称组的亚组。除了两个例外情况外，我们还看到，这种难题的解决方案始终是整个广义对称群体，也是索引二的两个特殊亚组之一。
Segerman's 15+4 puzzle is a hinged version of the classic 15-puzzle, in which the tiles rotate as they slide around. In 1974, Wilson classified the groups of solutions to sliding block puzzles. We generalize Wilson's result to puzzles like the 15+4 puzzle, where the tiles can rotate, and the sets of solutions are subgroups of the generalized symmetric groups. Aside from two exceptional cases, we see that the group of solutions to such a puzzle is always either the entire generalized symmetric group or one of two special subgroups of index two.
