三元系的大集問題.pdf

1、河北師范大學(xué)碩士學(xué)位論文三元系的大集問題姓名：程美慧申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：田子紅20080320AbstractAcollection(X，B1)，(x，島)，(x，島)ofqSTS(v)sisaAfoldlargesetofS11s(v)anddenotedbyLSTS；＼(v、ifevery3subsetofXiscontainedinexactlyASTS(v)softhecollectionItisindec

2、omposableanddenotedbyIDLSTSa(v)iftheredoesnotexistanLSTSx，(V)containedinthecollectionforanyⅣlandorders移蘭1or3(mod6)dothereexistanIDLSTSa(v)Inthefirstpartofthispaper，weusepartitionablecandelabrasystems(PCSs)andholeyAfoldla

3、rgesetofSTS(v)(HI。STS^(v))asauxiliarydesignstoestablisharecursiveconstructionforIDI。sTsA(u)ItshowsthatthereisanIDLSTSx(v)forA=5，6，釘三lor3(mod6)，andV≠3withtheonlypossibleexceptionIDLSTSx(7)AHybridtriplesystemoforderuHTS(v，

4、A)=(x，屢)，where侈isacollectionofcycleandtransitivetriplesofXsuchthateveryorderedpairofXbelongstOAtriplesof8AnoverlargesetofdisjointHTS(v，A)，denotedbyOLHTS(v，A)，isacollection(y＼∥)，4i))i，suchthatYisa(u1)set，each(y＼可)，A)isaHT

5、S(v，A)andallAsformapartitionofallcycleandtransitivetriplesofyInthelastpartofthispaperweshalldiscusstheexistenceproblemofOLHTS(v，A)andgivethefollowingconclusion：thereexistsanOLHTS(v，A)ifandonlyifA一1，2，4，釘三0，l(mod3)，andV≥4