若干組合序列的矩陣研究.pdf

1、大連理工大學(xué)博士學(xué)位論文若干組合序列的矩陣研究姓名：譚明術(shù)申請學(xué)位級別：博士專業(yè)：計算數(shù)學(xué)指導(dǎo)教師：王天明20040401AbstactWeintendtoinvestigatetherelationsbetweentheclassicalcombinatorialseqIleIleeSandtheirmatricesinthispaper，TheyarelistedaSfollows：1Thebinomialc。etficieIlts

2、(：：：)，端鬲(。)，(：：i)”dseq㈣n“、ank㈣tthatod。女=an_1，t—ianl，女a(chǎn)restudiedThecorrespondingmatricesandtheirpropertiesareinvestigatedSomevaluablecombinatorialidentitiesarederived2Lahnumberl(n，％)=㈤k／止(k型1)!anditsmatrix厶isstudiedTherel

3、ationsaIylolIgLahmatrices，PascalmatricesandStirlingmatricesareobtainedThefaetorizationsandpowersumformonLahmatricesaregiven3TheinatriceswithelementsG燦一／x)andtheirpropertieshavebeenstudiedcarefldlybymanymathematicians，whe

4、re妒”(z)arez”，z“|1andotherspecialformsrespectivelyInthispaper，thematricesLn㈦=(1(i，J)蛾一J(z))“nwithmoregellel氌1elementsareinvestigated，wheref(n，k)and妒，lx)satisfythefollowingrespectively：l(i，％)(％，J)：f(蜘)f：一A＼總一J／洲咖)=喜(批／㈤洲”)

5、k=0＼“Infact，妒n(z)isthepolynomialofbinomialtypeTherefore，theresultsweobtainedaremoregeneral4FibonaccisequencesareoflonghistoryandtheirapplicationsappearinmanyfieldsThefollowingbivariateFibonacciseqlIences(polyllomials)B)鏟