Riordan矩阵的中心系数矩阵及其应用
发布时间：2019-07-06 17:40
【摘要】：Riordan矩阵是组合数学中的主要研究对象之一,它是一类特殊的无穷下三角形矩阵,将该类型矩阵向左展开成等腰三角形矩阵,我们将这种矩阵称为ISO型三角形矩阵.ISO型三角形矩阵的中间列即为Riordan矩阵的中心系数,以它的中间列为初始列,取该矩阵的右半部分就是Riordan矩阵的中心系数矩阵.本文在此基础上,.通过多次重复上述过程定义了 Riordan矩阵的(m,r)-中心系数及(m,r)-中心系数矩阵.作为应用,在最后我们给出两类特殊的Riorda矩阵,即Pascal矩阵和Catalan矩阵,并得到一些恒等式.第一章,主要介绍了本课题的研究背景,并给出了 Riordan矩阵和Catalan矩阵的相关知识.第二章,首先给出Riordan矩阵的中心系数和r-中心系数的概念以及已有的研究成果,然后给出(m,r)-中心系数的概念以及它的生成函数.第三章,先介绍半.Riordan矩阵以及Riordan矩阵的r-中心系数矩阵,然后定义了 Riordan矩阵的(m,r)一中心系数矩阵,并且得到许多非常有意义的结果.文章的最后研究了 Pascal矩阵和Catalan矩阵的(m,r)-中心系数矩阵,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.
【学位授予单位】：兰州理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O151.21
本文编号：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.
【学位授予单位】：兰州理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O151.21
【参考文献】
相关硕士学位论文 前1条
1 郑赛男;Riordan矩阵的中心系数及其应用[D];兰州理工大学;2014年
，本文编号：2511213
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