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1、浙江省新昌中學(xué)作者:賈子涵張啟煊項(xiàng)羽銘指導(dǎo)老師:吳裕東對平面魔方群及其Cayley圖直徑的研究中國·浙江對平面魔方群及其Cayley圖直徑的研究摘要借鑒魔方的游戲規(guī)則,本文設(shè)計(jì)了一款游戲“平面魔方”,并運(yùn)用群論、計(jì)算機(jī)等工具對其性質(zhì)進(jìn)行了深入的挖掘.首先,本文對平面魔方的規(guī)則進(jìn)行了詳細(xì)介紹,其次,運(yùn)用群論的知識,本文研究了平面魔方的各個性質(zhì),如平面魔方置換群的階、Cayley圖直徑等,最后將模型推廣到異形并得出了一般性的結(jié)論.關(guān)鍵字:平面魔方置換群Cayley圖直徑1AbstractAccordingt
2、otherulesofmagiccube,theauthorshavedesignedatwo-dimensionmagiccubeinthispaper.Andtherulesofthecubeareexplainedintegrallty.Also,bymakinguseofgrouptheoryandthecomputer,theauthorsstudythepropertiesofthecube,suchastheorderofthepermutationgroupofthecube,thedi
3、ameterofCayleyGraph,etc.Theauthorsalsoextendthemodeltoirregularsituationsandthecommonresultsofthecubeareobtainedinthispaper.Keywords:two-dimensionmagiccube;permutationgroup;thediameterofCayleyGraph2目錄摘要Abstract1.基本介紹......................................
4、.................................................................................................11.1引言.....................................................................................................................................11.2平面魔方規(guī)則介紹......
5、.......................................................................................................11.3問題的提出.........................................................................................................................22.模型建立..............
6、.........................................................................................................................32.1群論基本介紹.....................................................................................................................32.2平面
7、魔方群.........................................................................................................................4三、的階.............................................................................................................................
8、.........5四、Cayley圖直徑..........................................................................................................................64.1Cayley圖的相關(guān)定義...............................................................
