A Note on Pascal's Matrix (original) (raw)
Gi-sang Cheon
JinSoo KimWe can get the Pascal's matrix of order n by taking the first n rows of Pascal's triangle and filling in with 0's on the right. In this paper we obtain some well known combinatorial identities and a factorization of the Stirling matrix from the Pascal's matrix.
Related papers
Extended Bernoulli and Stirling matrices and related combinatorial identities
Linear Algebra and its Applications, 2014
A generalization of the Pascal matrix and its properties
The linear algebra of the pascal matrix
Linear Algebra and its Applications, 1992
Factorial Stirling matrix and related combinatorial sequences
Linear Algebra and its Applications, 2002
2013
We prove certain identities involving Euler and Bernoulli polynomials that can be treated as recurrences. We use these and also other known identities to indicate connection of Euler and Bernoulli numbers with entries of inverses of certain lower triangular built of binomial coefficients. Another words we interpret Euler and Bernoulli numbers in terms of modified Pascal matrices.
The k-Fibonacci matrix and the Pascal matrix
Central European Journal of Mathematics, 2011
We prove certain identities involving Euler and Bernoulli polynomials that can be treated as recurrences. We use these and also other known identities to indicate strong connection between Euler and Bernoulli numbers and entries of inverses of certain lower triangular matrices built of binomial coe¢ cients. In other words we interpret Euler and Bernoulli numbers in terms of modi…ed Pascal matrices.
European Journal of Combinatorics, 2010
A factorization of the tribonacci matrix and the Pascal matrix
Applied Mathematical Sciences, 2017
The Akiyama–Tanigawa matrix and related combinatorial identities
Linear Algebra and its Applications, 2013
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.
Related papers
The linear algebra of the generalized Pascal functional matrix
Linear Algebra and its Applications, 1999
A very general binomial matrix
2021
Science China-mathematics, 2015
Extended symmetric Pascal matrices via hypergeometric functions
Applied Mathematics and Computation, 2004
Relation Between Stirling’s Numbers of the Second Kind and Tribonacci Matrix
2018
Factorizations of the Pascal Matrix via a Generalized Second Order Recurrent Matrix
Istanbul University - DergiPark, 2009
Further Combinatorial Identities Deriving from the n-th Power of a 2times22 \times 22times2 Matrix
Linear recurrences associated to rays in Pascal’s triangle and combinatorial identities
Mathematica Slovaca, 2014
Tetranacci Matrix via Pascal's Matrix
2017
A Note on a Family of Generalized Pascal Matrices Defined by Riordan Arrays
Further combinatorial identities deriving from the nth power of a 2×2 matrix
Discrete Applied Mathematics, 2006
Matrix powers of column-justified Pascal triangles and Fibonacci sequences
2000
Diagonal Sums in the Pascal Pyramid, II: Applications
J. Integer Seq., 2019
A Note on Pascal's Triangle and Its Applications
IAETSD JOURNAL FOR ADVANCED RESEARCH IN APPLIED SCIENCES, 2019
POWERS OF A MATRIX AND COMBINATORIAL IDENTITIES 1
Spectral Properties of a Binomial Matrix
2000
A three by three Pascal matrix representations of the generalized Fibonacci and Lucas sequences
Hacettepe Journal of Mathematics and Statistics
Combinatorial Identities Deriving from the n-th Power of a 2times22 \times 22times2 Matrix
An identity of Andrews and a new method for the Riordan array proof of combinatorial identities
Discrete Mathematics, 2008
A connection between a generalized Pascal matrix and the hypergeometric function
Applied Mathematics Letters, 2003
Ballot matrix as Catalan matrix power and related identities
Discrete Applied Mathematics, 2012
Generalized Stirling Numbers, Exponential Riordan Arrays, and Orthogonal Polynomials
2011