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Linear Algebra and Its Applications, ISSN 0024-3795, 2011, Volume 434, Issue 10, pp. 2187 - 2196
Let Ω m , n ( α , β , γ ) denote a set of all elements of weighted lattice paths with weight ( α , β , γ ) in the xy-plane from ( 0 , 0 ) to ( m , n ) such... 
Weighted lattice path | Lattice path matrix | Positive definite | LDU decomposition | Generalized Pascal matrix | MATHEMATICS, APPLIED
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 2007, Volume 423, Issue 2, pp. 230 - 245
In this paper, we introduce the generalized Pascal functional matrix and show that the existing variations of Pascal matrices are special cases of this... 
Generalizing functions | Generalized Pascal functional matrix | Combinatorial identities | LU decomposition | Pascal matrices | MATHEMATICS, APPLIED | LINEAR ALGEBRA | ALGEBRAIC PROPERTIES | generalized Pascal functional matrix | combinatorial identities | generalizing functions
Journal Article
Communications in Statistics - Theory and Methods, ISSN 0361-0926, 07/2015, Volume 44, Issue 13, pp. 2738 - 2752
Journal Article
by Zhang, LM and Sun, ZH and Qu, XY and Zhao, XQ
LINEAR ALGEBRA AND ITS APPLICATIONS, ISSN 0024-3795, 09/2019, Volume 577, pp. 214 - 239
Let B-n = [B-n,B-k](n,k)>= 0 be the Bell matrix. Define the n x n shift Bell matrix P-n,P-k by (P-n,P-k)(i,j) = B-k+i-1,B-kj-1 for j = 1, 2, ... n and k = 0,... 
MATHEMATICS | MATHEMATICS, APPLIED | IDENTITIES | NUMBERS | Bell polynomials | Generalized Riordan array | TRIANGLES | n x n shift iteration matrix | GENERALIZED PASCAL MATRIX | n x n shift Bell matrix
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2017, Volume 446, Issue 1, pp. 87 - 100
This paper deals with a unified matrix representation for the Sheffer polynomials. The core of the proposed approach is the so-called creation matrix, a... 
Binomial type polynomials | Generalized Pascal matrix | Sheffer polynomials | Appell polynomials | Creation matrix | MATHEMATICS | DETERMINANTAL APPROACH | MATHEMATICS, APPLIED | BELL POLYNOMIALS | SEQUENCES | IDENTITIES
Journal Article
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN 0302-9743, 2017, Volume 10405, pp. 409 - 421
Conference Proceeding
Electronic Journal of Linear Algebra, ISSN 1081-3810, 01/2009, Volume 18, pp. 564 - 588
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 2009, Volume 225, Issue 1, pp. 309 - 315
In this paper, we give an algorithm for solving linear systems of the Pascal matrices. The method is based on the explicit factorization of the Pascal... 
Pascal matrix | Generalized Pascal matrix | Toeplitz matrix | Factorization | Algorithm | Linear systems | Algorithms
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 02/2015, Volume 253, pp. 83 - 101
A simple but elegant method was adopted in Youn and Yang (2011) in order to derive a differential equation and recursive formulas for Sheffer polynomials.... 
Generalized Pascal functional matrix | Umbral calculus | Wronskian matrix | Sheffer sequences | MATHEMATICS, APPLIED | NUMBERS
Journal Article
International Journal of Computer Mathematics, ISSN 0020-7160, 10/2016, Volume 93, Issue 10, pp. 1756 - 1770
Journal Article
Mediterranean Journal of Mathematics, ISSN 1660-5446, 10/2019, Volume 16, Issue 5, pp. 1 - 20
In this contribution, some new identities involving Sheffer–Appell polynomial sequences using generalized Pascal functional and Wronskian matrices are deduced.... 
33C45 | identities | 15A24 | generalized Pascal functional | Mathematics, general | Mathematics | Wronskian matrices | 15A15 | Sheffer–Appell polynomial sequence | orthogonal polynomials | MATHEMATICS | DETERMINANTAL APPROACH | MATHEMATICS, APPLIED | APOSTOL-BERNOULLI | Sheffer-Appell polynomial sequence
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 03/2014, Volume 444, pp. 114 - 131
In this paper we establish plenty of number theoretic and combinatoric identities involving generalized Bernoulli polynomials and Stirling numbers of both... 
Bernoulli matrix | Bernoulli polynomials | Pascal matrix | Stirling numbers | Hyperharmonic numbers | Stirling matrix | MATHEMATICS, APPLIED | DEGENERATE BERNOULLI | NUMBERS | POLYNOMIALS | LINEAR ALGEBRA | ALGEBRAIC PROPERTIES | GENERALIZED PASCAL MATRIX | FUNCTIONAL MATRIX | Mathematics - Number Theory
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 08/2008, Volume 156, Issue 15, pp. 3040 - 3045
In this paper, we study the Jordan canonical form of the generalized Pascal functional matrix associated with a sequence of binomial type, and demonstrate that... 
Sequence of binomial type | Generalized Pascal functional matrix | Bell polynomial | Jordan canonical form | Pascal matrix | Iteration matrix | Stirling number | MATHEMATICS, APPLIED | LINEAR ALGEBRA | STIRLING MATRIX | FUNCTIONAL MATRIX
Journal Article
Science China Mathematics, ISSN 1674-7283, 5/2019, Volume 62, Issue 5, pp. 999 - 1028
In this paper, we derive five basic identities for Sheffer polynomials by using generalized Pascal functional and Wronskian matrices. Then we apply twelve... 
11B83 | 05A40 | degenerate Bernoulli polynomial | Krobov polynomial of the first kind | 05A19 | Mathematics | generalized Pascal functional matrix | Applications of Mathematics | Wronskian matrix | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 2011, Volume 217, Issue 22, pp. 9122 - 9132
In this paper we use the Catalan matrix power as a tool for deriving identities involving Catalan numbers and hypergeometric functions. For that purpose, we... 
Catalan matrix power | Pascal matrix | Catalan numbers | Catalan matrix | Hypergeometric identities | Generalized hypergeometric function | MATHEMATICS, APPLIED | COMBINATORIAL IDENTITIES | FIBONACCI | Hypergeometric functions | Pascal (programming language) | Simplification | Computation | Mathematical analysis | Tools | Mathematical models
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 2009, Volume 215, Issue 2, pp. 796 - 805
We introduce the notion of the Catalan matrix C n [ x ] whose non-zero elements are expressions which contain the Catalan numbers arranged into a lower... 
Pascal matrix | Combinatorial identities | Catalan numbers | Catalan matrix | Generalized hypergeometric function | Euler gamma function | MATHEMATICS, APPLIED | FIBONACCI
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 2008, Volume 156, Issue 14, pp. 2793 - 2803
In this paper, we study the relations between the Bell matrix and the Fibonacci matrix, which provide a unified approach to some lower triangular matrices,... 
Generalized Fibonacci numbers | Combinatorial identities | Iteration matrix | Fibonacci numbers | Bell polynomials | POLYNOMIALS | MATHEMATICS, APPLIED | LINEAR ALGEBRA | GENERALIZED PASCAL MATRIX | STIRLING MATRIX
Journal Article
UTILITAS MATHEMATICA, ISSN 0315-3681, 09/2017, Volume 104, pp. 47 - 66
There are scattered results in the literature showing that the leading principal minors of certain infinite integer matrices form the Fibonacci and Lucas... 
MATHEMATICS, APPLIED | Lucas sequence | Recurrence relation | Fibonacci sequence | Determinant | STATISTICS & PROBABILITY | Matrix factorization | Toeplitz matrix | Jacobsthal sequence | Generalized Pascal triangle | Pell sequence | 7-matrix | TOEPLITZ | FIBONACCI
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 04/2015, Volume 471, pp. 569 - 574
In a recent article in this journal Deveci and Karaduman [3] proposed several conjectures (two of which have been proven by Hiller [4]) regarding the order of... 
Order of cyclic groups | Integer matrices | Generalized Pascal matrices | Primes | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
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