區(qū)組大小為3的最優(yōu)循環(huán)填充.pdf

1、蘇州大學(xué)碩士學(xué)位論文區(qū)組大小為3的最優(yōu)循環(huán)填充姓名：張晗申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：王健敏20090501OptimalCyclicPackingswithBlockSizeThreeAbstractOptimalCyclicPackingswithBlockSizeThreeAbstractLetu，k，Abepositiveintegersand移≥七A(u，七，入)一packingisapair(V8)，whereV

2、isavsetofelements(points)and召isacollectionofksubsetsofV(blocks)，suchthateverypairofpointsoccursinatmost入blocksin召，denotedbyCP(k，入；u)AnautomorphismofaP(k，A；“)，(V層)，isabijeztion砂：V—V，suchtahttheinducedmapping盯：召_崢Bisalsoab

3、ijectionAP(k，入；u)iscyclicifitadmitsacyclicautomorphismgroupoforderuthatisspannedbyau—cycleAcyclicP(k，A；u)havingonlyfullblockorbitsisdenotedbycP(k，A；可)AcyclicP(k，入；口)issaidtobeoptimalifithasmaximumpossiblenumberofbasebloc

4、ks，whichiscalledcyclicpackingnumberInparticular，thecyclicpackingnumberofCP(k，入；u)isdenotedbyCD(v，七，入)。Ifeverypairofpointsoccursinexactly入blocks，thedesignisreferredtoasacyclicbalancedincompleteblockdesign，denotedbyCB(k，A；

5、t，)ErnieFBrickellandVictorKWei[7】havedeterminedthecyclicpackingnumbersCD(v，3，1)for入1，MJColbournandCJColbourn【20】havedeterminedtheexistenceofaCB(3，入；口)Inthispaper，weresearchtheexistenceofoptimalCP(3，入；“)withA1，anddetermin

6、ethecyclicpackingCD(v，3，A)，ie，f【掣卜l，ifv三10(mod12)andA三2(rood12)，CD(v，3，入)=orif“蘭6，12(rood24)and入墨5(mod12)，orifu三2(rood4)and入三6(rood12)，orifu三2(rood24)and入三7(mod12)，orifu三18(mod24)and入三11(rood12)，【掣J，otherwiseKeywords：Cyc