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Two Kinds of Numbers and Their Applications

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Acta Mathematica Sinica,English Series 2006年第4期22卷 999-1006页

作者： Zhi Zheng ZHANG Hong FENG Department of Mathematics Luoyang Teachers' College Luoyang 471022 P. R. China College of Mathematics and Information Science Henan University Kaifeng 475001 P. R. China Department of Applied Mathematics Dalian University of Technology Dalian 116024 P. R. China

C. Radoux （J. Comput. Appl. Math., 115 （2000） 471-477） obtained a computational formula of Hankel determinants on some classical combinatorial sequences such as Catalan numbers and polynomials, Bell polynomials, Hermite polynomials, Derangement polynomials etc. From a pair of matrices this paper introduces two kinds of numbers. Using the first kind of numbers we give a unified treatment of Hankel determinants on those sequences, i.e., to consider a general representation of Hankel matrices on the first kind of numbers. It is interesting that the Hankel determinant of the first kind of numbers has a close relation that of the second kind of numbers.

关键词： combinatorial sequence Hankel determinant combinatorial identity

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Some Notices on Mina Matrix and Allied Determinant Identities

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Journal of Mathematical Research with Applications 2016年第3期36卷 253-264页

作者： Jin WANG Xinrong MA Department of Mathematics Soochow University

By means of a special LU factorization of the Mina matrix with the n-th row and k-th column entry D;(f;（x）), we obtain not only a short proof of the Mina determinant identity but also the inverse of the Mina matrix. Finally, by use of some similar factorizations built on the Lagrange interpolation formula, two new determinant identities of Mina type are established.

关键词： Mina determinant identity Mina matrix LU factorization derivative operator inverse combinatorial identity Lagrange interpolation Melzak’s formula

A Nonlinear Expression for Fibonacci Numbers and Its Consequences

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Journal of Mathematical Research with Applications 2012年第6期32卷 654-658页

作者： Leetsch C. HSU School of Mathematical Sciences Dalian University of Technology

Here investigated is a kind of nonlinear combinatorial expression involving Fibonacci numbers defined on the set of integers. A number of particular consequences will be presented as examples.

关键词： difference operator combinatorial identity congruence relation.

The Algebraic Properties of a Type of Infinite Lower Triangular Matrices Related to Derivatives

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Journal of Mathematical Research and Exposition 2002年第4期22卷 549-554页

作者：赵熙强王天明南京航空航天大学空气动力学系江苏南京210016 大连理工大学应用数学系辽宁大连116024

In this paper, Jabotinsky matrices in [4, 5] are modified and a type of infinite lower triangular matrices T(f) is discussed. Some algebraic properties of T(f) are obtained and proved. Additionally, some inverse pairs... 详细信息

关键词： Jabotinsky matrix combinatorial identity inverse pair derivative.

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Two Kinds of Series Involving the Reciprocals of Binomial Coefficients

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Chinese Quarterly Journal of Mathematics 2011年第2期26卷 306-310页

作者： SONG Hai-tao Department of Engineering Technology Xinxiang Vocational and Technical College Xinxiang 453006China

By applying the theory of formal power series,the author obtains the closed forms for two kinds of infinite series involving the reciprocals of binomial coefficients,and the author gets another closed form for the inf... 详细信息

关键词： reciprocals of binomial coefficients formal power series combinatorial identity

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