Solving puzzles related to permutation groups
Solving puzzles related to permutation groups
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解决与排列群相关的难题
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
Markus Püschel
中科院分区：
文献类型：
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作者：
S. Egner;Markus Püschel
可以解决的置换群的方法的物理难题被认为是和分类艾德根据一些抽象的属性。解决方案的方法是基于字稳定器链（横向元素是在一个给定的列表中的发电机的话）。提出了新的方法来构建单词稳定器链，利用物理谜题中存在的特殊结构。在许多情况下，该方法成功地避免了困扰稳定链方法来构建横向元素的字长的指数增长。最后，给出了一个谜题的分类方案，该方案有助于确定与谜题相关的置换群。
Physical puzzles that can be solved with methods for permutation groups are considered and classi ed according to a number of abstract properties. The approach for solution is based on word stabilizer chains (the transversal elements are factored in words in a given list of generators). New methods are presented to construct word stabilizer chains that take advantage of the special structures present in physical puzzles. In many cases the methods are successful in avoiding the exponential growth of word length that plagues stabilizer chain methods to construct transversal elements. Finally, a classi cation scheme for puzzles is presented which helps with nding the permutation group related to the puzzle.