A Note on a Family of Generalized Pascal Matrices Defined by Riordan Arrays

Barry, Paul (2013) A Note on a Family of Generalized Pascal Matrices Defined by Riordan Arrays. Journal of Integer Sequences, 16. ISSN 1530-7638

[img]
Preview
PDF
barry231.pdf

Download (205kB) | Preview
Official URL: https://cs.uwaterloo.ca/journals/JIS/VOL16/Barry2/...

Abstract

We study the properties of a parameterized family of generalized Pascal matrices, defined by Riordan arrays. In particular, we characterize the central elements of these lower triangular matrices, which are analogues of the central binomial coefficients. We then specialize to the value 2 of the parameter, and study the inverse of the matrix in question, and in particular we study the sequences given by the first column and row sums of the inverse matrix. Links to moments and orthogonal polynomials are examined, and Hankel transforms are calculated. We study the effect of the powers of the binomial matrix on the family. Finally we posit a conjecture concerning determinants related to the Christoffel-Darboux bivariate quotients defined by the polynomials whose coefficient arrays are given by the generalized Pascal matrices.

Item Type: Article
Departments or Groups: *NONE OF THESE*
Divisions: School of Science
Depositing User: Paul Barry
Date Deposited: 28 May 2013 16:33
Last Modified: 22 Aug 2016 10:26
URI: http://repository.wit.ie/id/eprint/2655

Actions (login required)

View Item View Item