Please use this identifier to cite or link to this item:
https://ah.lib.nccu.edu.tw/handle/140.119/32561| DC Field | Value | Language |
|---|---|---|
| dc.contributor.advisor | 陳永秋<br>李陽明 | zh_TW |
| dc.contributor.author | 施耀振 | zh_TW |
| dc.contributor.author | Shih,Yaio-Zhern | en_US |
| dc.creator | 施耀振 | zh_TW |
| dc.creator | Shih,Yaio-Zhern | en_US |
| dc.date | 2006 | en_US |
| dc.date.accessioned | 2009-09-17T05:45:12Z | - |
| dc.date.available | 2009-09-17T05:45:12Z | - |
| dc.date.issued | 2009-09-17T05:45:12Z | - |
| dc.identifier | G0089751501 | en_US |
| dc.identifier.uri | https://nccur.lib.nccu.edu.tw/handle/140.119/32561 | - |
| dc.description | 博士 | zh_TW |
| dc.description | 國立政治大學 | zh_TW |
| dc.description | 應用數學研究所 | zh_TW |
| dc.description | 89751501 | zh_TW |
| dc.description | 95 | zh_TW |
| dc.description.abstract | 在這篇論文，我們主要探討兩個獨立的組合數學主題：一個是Hadamard矩陣的建構，一個是有關森林的研究。在第一個主題，所得者又分為二，其一，我們從一個已知的Hadamard矩陣，利用Sylvester的方法去建構名為Jm-Hadamard矩陣。從這個矩陣裡，藉由在Sm上適當的排列，可以獲致其他2mm!-1個Hadamard矩陣。另外，我們引進Jm-class的概念， 將之寫成CJm，並探討當n整除n`時，CJn`是否包含於CJn。關於這個問題，我們得到最初的結論是CJ8 CJ4 CJ2。其二，在已知的t個階數分別是4m1，4m2，…，4mt的Hadamard矩陣，希望獲得一個階數是2km1m2… mt的Hadamard矩陣，使得k值愈小愈好。我們可以找到最小指數的上界，這個數稍好於Craigen及de Launey所得到的值。在第二個主題裡，我們致力於三個目標，首先，我們將平面樹上的一些結果，推廣到平面森林上，諸如Shapiro的結果，葉子的偶數、奇數問題，Catalan數與類似數之間的恒等式。其二，我們用了一個很簡潔的方法去證明Chung-Feller定理，也獲致相關的結果及應用。最後，我們以研究數種n-caterpillars的優美標法，作為本文的結束，最特別的是我們可藉用拉丁方陣去建構2n-caterpillars的優美標法。 | zh_TW |
| dc.description.tableofcontents | Abstract\n中文摘要\nIntroduction\nI Constructions of Hadamard Matrices\n1 On Jm-Hadamard Matrices\n 1.1 Jm-Hadamard Matrices\n 1.2 Counterexamples\n2 Further Results on Jm-Hadamard Matrices\n 2.1 Some Properties of Jm-Hadamard Matrices\n 2.2 Hadamard Matrices in Jm-classes\n3 On Craigen-de Launey’s Constructions of Hadamard Matrices\n 3.1 Generalizations of Craigen’s Theorem and Craigen-Seberry-Zhang’s Theorem\n 3.2 Minimum Exponent of Hadamard Matrices Resulting from t Hadamard Matrices\nII Studies of Forests \n4 On Enumeration of Plane Forests\n4.1 A Catalan Identity \n4.2 Some Results of Leaves\n4.3 Generalizations of Motzkin-Catalan Identity\n4.4 Some Riordan Families\n5 The Chung-Feller Theorem Revisited\n5.1 A Simple Proof of Chumg-Feller Theorem\n5.2 Bi-color Plane Forests\n5.3 Semiatandard Tableaux and Noncrossing Semiordered Pairs\n5.4 Motzkin Paths with Flaws and a Labelled Minimum\n6. Graceful Labellings of Some n-Caterpillars\n6.1 Graceful Labellings of 2-Caterpillars\n6.2 Graceful Labellings of (r,m,n)-Caterpillars\n6.3 n-Partition with Parameter k\n6.4 Latin Squares and Graceful Labellings of 2n-Caterpillars\nConcluding Remarks\nBibliograghy | zh_TW |
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| dc.language.iso | en_US | - |
| dc.source.uri | http://thesis.lib.nccu.edu.tw/record/#G0089751501 | en_US |
| dc.subject | Kronecker乘積 | zh_TW |
| dc.subject | Sylvester-Hadamard矩陣 | zh_TW |
| dc.subject | J_m-Hadamard矩陣 | zh_TW |
| dc.subject | 正交對 | zh_TW |
| dc.subject | Weighing矩陣 | zh_TW |
| dc.subject | 最小指數 | zh_TW |
| dc.subject | 平面森林 | zh_TW |
| dc.subject | Catalan數 | zh_TW |
| dc.subject | Motzkin數 | zh_TW |
| dc.subject | Riordan數 | zh_TW |
| dc.subject | Narayana數 | zh_TW |
| dc.subject | Dyck路徑 | zh_TW |
| dc.subject | Motzkin路徑 | zh_TW |
| dc.subject | Chung-Feller定理 | zh_TW |
| dc.subject | 優美標法 | zh_TW |
| dc.subject | 拉丁方陣 | zh_TW |
| dc.subject | J_m-classes | en_US |
| dc.subject | n-Caterpillars | en_US |
| dc.title | 兩個組合數學的主題： Hadamard 矩陣的建構及有關森林的研究 | zh_TW |
| dc.title | Two Combinatorial Topics: Constructions of Hadamard Matrices and Studies of Forests | en_US |
| dc.type | thesis | en |
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