Riordan矩陣的中心系數矩陣及其應用
發(fā)布時間：2019-07-06 17:40
【摘要】：Riordan矩陣是組合數學中的主要研究對象之一,它是一類特殊的無窮下三角形矩陣,將該類型矩陣向左展開成等腰三角形矩陣,我們將這種矩陣稱為ISO型三角形矩陣.ISO型三角形矩陣的中間列即為Riordan矩陣的中心系數,以它的中間列為初始列,取該矩陣的右半部分就是Riordan矩陣的中心系數矩陣.本文在此基礎上,.通過多次重復上述過程定義了 Riordan矩陣的(m,r)-中心系數及(m,r)-中心系數矩陣.作為應用,在最后我們給出兩類特殊的Riorda矩陣,即Pascal矩陣和Catalan矩陣,并得到一些恒等式.第一章,主要介紹了本課題的研究背景,并給出了 Riordan矩陣和Catalan矩陣的相關知識.第二章,首先給出Riordan矩陣的中心系數和r-中心系數的概念以及已有的研究成果,然后給出(m,r)-中心系數的概念以及它的生成函數.第三章,先介紹半.Riordan矩陣以及Riordan矩陣的r-中心系數矩陣,然后定義了 Riordan矩陣的(m,r)一中心系數矩陣,并且得到許多非常有意義的結果.文章的最后研究了 Pascal矩陣和Catalan矩陣的(m,r)-中心系數矩陣,并得到一些恒等式.
[Abstract]:Riordan matrix is one of the main research objects in combinatorial mathematics. It is a special kind of infinite lower triangular matrix. This type of matrix is expanded to the left into isosceles triangular matrix. We call this matrix ISO triangular matrix. The middle column of ISO triangular matrix is the central coefficient of Riordan matrix, and the right half of the matrix is the central coefficient matrix of Riordan matrix. On this basis,. The (m, r)-center coefficient and (m, r)-center coefficient matrix of Riordan matrix are defined by repeating the above process many times. As an application, at last, we give two kinds of special Riorda matrices, namely Pascal matrix and Catalan matrix, and obtain some identities. In the first chapter, the research background of this subject is introduced, and the related knowledge of Riordan matrix and Catalan matrix is given. In chapter 2, the concepts of center coefficient and r-center coefficient of Riordan matrix and the existing research results are given, and then the concept of (m, r)-center coefficient and its generating function are given. In chapter 3, the r-central coefficient matrix of semi-Riordan matrix and Riordan matrix is introduced, and then the (m, r) central coefficient matrix of Riordan matrix is defined, and many very meaningful results are obtained. At the end of this paper, we study the (m, r)-central coefficient matrix of Pascal matrix and Catalan matrix, and obtain some identities.
【學位授予單位】：蘭州理工大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O151.21
本文編號：2511213
[Abstract]:Riordan matrix is one of the main research objects in combinatorial mathematics. It is a special kind of infinite lower triangular matrix. This type of matrix is expanded to the left into isosceles triangular matrix. We call this matrix ISO triangular matrix. The middle column of ISO triangular matrix is the central coefficient of Riordan matrix, and the right half of the matrix is the central coefficient matrix of Riordan matrix. On this basis,. The (m, r)-center coefficient and (m, r)-center coefficient matrix of Riordan matrix are defined by repeating the above process many times. As an application, at last, we give two kinds of special Riorda matrices, namely Pascal matrix and Catalan matrix, and obtain some identities. In the first chapter, the research background of this subject is introduced, and the related knowledge of Riordan matrix and Catalan matrix is given. In chapter 2, the concepts of center coefficient and r-center coefficient of Riordan matrix and the existing research results are given, and then the concept of (m, r)-center coefficient and its generating function are given. In chapter 3, the r-central coefficient matrix of semi-Riordan matrix and Riordan matrix is introduced, and then the (m, r) central coefficient matrix of Riordan matrix is defined, and many very meaningful results are obtained. At the end of this paper, we study the (m, r)-central coefficient matrix of Pascal matrix and Catalan matrix, and obtain some identities.
【學位授予單位】：蘭州理工大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O151.21
【參考文獻】
相關碩士學位論文 前1條
1 鄭賽男;Riordan矩陣的中心系數及其應用[D];蘭州理工大學;2014年
，本文編號：2511213
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