Pólya 计数法的应用
南京外国语学校 陈瑜希
目录
Pólya 计数法的应用...................................................................................................................1
目录.............................................................................................................................................1
摘要.............................................................................................................................................2
关键字.........................................................................................................................................2
问题的提出.................................................................................................................................2
[例一] He's Circles SGU294...............................................................................................2
[分析]..........................................................................................................................2
预备知识.....................................................................................................................................3
群.........................................................................................................................................3
置换.....................................................................................................................................3
置换群.................................................................................................................................3
Burnside 引理..............................................................................................................................4
介绍.....................................................................................................................................4
证明.....................................................................................................................................4
Pólya 计数法...............................................................................................................................7
介绍.....................................................................................................................................7
证明:.................................................................................................................................8
应用.............................................................................................................................................8
[例二]Cubes UVA 10601....................................................................................................8
[分析].........................................................................................................................9
[例三]Transportation is fun SPOJ 419 SPOJ422..............................................................9
[分析].......................................................................................................................10
[例四]SGU282 Isomorphism...........................................................................................11
[分析]........................................................................................................................11
总结...........................................................................................................................................13
参考文献...................................................................................................................................14
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