24 citations · 74 across the 56 of their papers we have counts for
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Riordan Pseudo-Involutions, Continued Fractions and Somos Sequences
Paul Barry
We define a three parameter family of Bell pseudo-involutions in the Riordan group. The defining sequences have generating functions that are expressible as continued fractions. We…
On the -Matrices of Pascal-like Triangles Defined by Riordan Arrays
Paul Barry
We define and characterize the -matrices associated to Pascal-like matrices that are defined by ordinary and exponential Riordan arrays. These generalize the face matrices of si…
A note on number triangles that are almost their own production matrix
Paul Barry
We characterize a family of number triangles whose production matrices are closely related to the original number triangle. We study a number of such triangles that are of combinat…
The -Vectors of Pascal-like Triangles Defined by Riordan Arrays
Paul Barry
We define and characterize the -matrix associated to Pascal-like matrices that are defined by ordinary and exponential Riordan arrays. We also define and characterize the -ma…
The -Eulerian Polynomials as Moments, via Exponential Riordan Arrays
Paul Barry
Using the theory of exponential Riordan arrays, we show that the -Eulerian polynomials are moments for a paramaterized family of orthogonal polynomials. In addition, we show t…
Generalized Eulerian Triangles and Some Special Production Matrices
Paul Barry
We show how some special production matrices may be used to define families of generalized Eulerian triangles. We furthermore show that these generalized Eulerian triangles are the…