偏序集理论在拟阵论中的应用

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1、西安电子科技大学博士学位论文偏序集理论在拟阵论中的应用姓名：毛华申请学位级别：博士专业：应用数学指导教师：刘三阳20020601映射是不能取代强映射的．这可以从二者对交换定理的反映上看出。此结论也表明研究强映越的必要性．由于区间广义拟阵是广义拟阵中应用广泛的一个大家族，故文中专门给出了关于它的囱同构的刿定方法．‘(5)运用先分类、后分鹰的办法，对给定有限巢上的全体拟阵掇出了一种构造方法：借助偏序集理论，建立起给定有限集上全体拟阵与嬲论中树的联系，从丽得到了另一种寻我给定有黻集上全体叛阵的构造方法．这两种方法使得拟阵可以运用到寻找概念格

2、的研究中，也使褥拟阵理论与概念格理论的关系更为密切．关键词：偏序集群拟阵偏痔黛毅簿广义拟阵IlAbstractMatroidswereinventedaround1930．Unfortunately，theclassicalnotionsofmalroidsarenotsmtedtothecontemporarycommandswiththeadventanddevelopmentofscientifictechnologyespeciallycomputerscience．Basedonthis，theworkofthegenera

3、lizationoftheclassicalmatroidsisimperative．Thisworkisdoneinmanyways，themostfamousandrepresentativearcthefollowing,oneisposetmalroidthatcomesfromreplacingtheunderlyingsetofamatroidbyapartiallyorderedset；anotherisgreedoiddefineaasacollectionsatisfyinganorderedversionofthe

4、matroidaxioms．Eventoday．thenewtwotheoriesarcdevelopingcontinuously．Alookatthehistoryofmatroidsmightleadtotheconclusionthatjuststudiedfromdifferentdirections，matroidtheoryhasbeenrichinconnectionswithpureandapplied,deeplyrootedintheutmostreachesofexperimentalthinking．Inad

5、dition，forthetheoryofbothposetmalroidsandgreedoids．posettheorywasoneofthekeysoBrces．Soitisnotsurprisingthatinthisdissertation，withthehelpofposettheory，thetwonewtheoriesarepolishedandrefmedindifferentmethodsthataredistinctfromformerscholars．Atthesametime，somepropertiesof

6、matroidsareextendedinmanywayswithoutlosingsomeofthestyleandfeaturesoftheseconcepts．Somerelationshipsbetweenthetwonewtheoriesarediscussedtoo．Allthesea∞polishingandrefiningonthenewtwotheories．Antimatroidsasaclassof蓼eedoidsarcinmanyrespects‘‘antipodal”tomatroids．Thusitisna

7、turaltoconsiderandstudyonantimatmidswhenresearchintothepropertiesofgreedoids．Besides，itisknownthatconeeptlatticeisoneofalleffecfivemathematicaltoolforthestudyofdatamininganddataanalysis．TheapplicationofmalToidtheoryintoitisanewideaandanewmethodintheresearchofconceptlatt

8、ice．Themainresultsasfollows．(1)Foursubmatroids—truncation，elongation，restrictionandcontractionareextendedfromm