24 citations · 74 across the 56 of their papers we have counts for
8 papers · 2 filters
Chebyshev moments and Riordan involutions
Paul Barry
We show that the coefficient array of a family of Chebyshev moments defines an involution in the group of Riordan arrays. We then extend this result to certain families of -orth…
Riordan arrays, the -matrix, and Somos sequences
Paul Barry
We characterize certain Riordan arrays by their -matrices and sequences. We conjecture the form of a generic -matrix which leads to Somos sequences. We find an -ma…
A Note on Riordan Arrays with Catalan Halves
Paul Barry
For a lower triangular matrix we call the matrices with respective entries and the vertical and the horizontal halves. In this note, we di…
Generalized Catalan recurrences, Riordan arrays, elliptic curves, and orthogonal polynomials
Paul Barry
We show that the Catalan-Schroeder convolution recurrences and their higher order generalizations can be solved using Riordan arrays and the Catalan numbers. We investigate the Han…
On the halves of a Riordan array and their antecedents
Paul Barry
Every Riordan array has what we call a horizontal half and a vertical half. These halves of a Riordan array have been studied separately before. Here, we place them in a common con…
Constant coefficient Laurent biorthogonal polynomials, Riordan arrays and moment sequences
Paul Barry
We study properties of constant coefficient Laurent biorthogonal polynomials using Riordan arrays. We give details of related orthogonal polynomials, and we explore relationships b…