區(qū)組大小為4的有向BIBD的嵌入.pdf

1、蘇州大學(xué)碩士學(xué)位論文區(qū)組大小為4的有向BIBD的嵌入姓名：殷曉暉申請學(xué)位級(jí)別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：殷劍興2002.4.1皇墮竺!————————————蘭EmbeddingsofDirectedBIBDswithBlockSizeFourAbstractAtransitix，elvorderedktuple(ol，d2，一，nk)isdefinedtObetheset(Uiaj)：1iJkconsistingof女(≈一1)／2

2、orderedpairsAdirectedbalancedin(‘ompleteblockdesign(DBIBDlwithordervblo(ksize＆andindex^，denotedbyDB(kA：u)，isaDair(X4)，where工isasetofl，pointsandAisacollectionoftransitix’e13’orderedktuplesfcalledblockslofY，suchthatea(‘hor

3、deredpairofdistinctpointsofYOccurs(xa(t13’inAblocksLetf一A)beaDB(k，A；“)and(】jB)aDB(k，A；to)IfyC一一and8CA，ltl㈨(】iB1issaidtObeanembeddingof(一4)，or(1j8)isasubdesignof(、，A)、、PusenotationDB。(k，A：”)todenoteaDB(k，A；“)containingaDB

4、(kA：ltl)asitSsubdesignT11egoalofthispaperistOdelermineforwhatvaluesofV，叫andAthereex—istSaDB。(4，A：u)Itisobx’iousthatthenecessaryconditionsoftheexistenceofaDBw(4，A；u)arethat“23w十1，andA(”一1)，A(Ⅲ一1)三0(rood3)Sotocompletetheex

5、istenceproblemofaDB”(4，A；u)witharbitraryA，weonlyneedtOdealwiththecaseA∈f1，3Itisprovedinthispaperthatif“24w1，theabox’eneces—sarvconditionsoftheexistenceofaDB口(4，1；u)andaDBⅦ(4，3；73)arealsosufficientAIldwhen3w1≤u≤4w，wedisti