5 papers · 1 filter
Elliptic Curves, Riordan arrays and Lattice Paths
Paul Barry
In this note, we show that to each elliptic curve of the form we can associate a family of lattice paths whose step set is determined by the parameters o…
-orthogonal polynomials, Fuss-Catalan matrices and lattice paths
Paul Barry
In this note, we show how to define certain Riordan arrays, that we call the Fuss-Catalan-Riordan arrays, by means of a special family of -orthogonal polynomials. We relate the…
Notes on Riordan arrays and lattice paths
Paul Barry
In this note, we explore links between Riordan arrays and lattice paths. We begin by describing Riordan arrays, and some of their generalizations, including rectifications and tria…
The Triple Riordan Group
Paul Barry
We define the triple Riordan group, whose elements consist of -tuples of power series with , and $f_1, f_2, f_3 \in x\mathbf{R}[[x^3…
A Riordan array family for some integrable lattice models
Paul Barry
We study a family of Riordan arrays whose square symmetrizations lead to the Robbins numbers as well as numbers associated to the vertex model. We provide closed-form expressi…