Riordan's Arrays and Two-Dimensional Difference Equations

TL;DR

This paper explores rational Riordan's arrays through combinatorial analysis, modeling them as solutions to two-dimensional difference equations and investigating their asymptotic behavior.

Contribution

It introduces a novel approach linking Riordan's arrays to two-dimensional difference equations and analyzes their asymptotic properties.

Findings

Representation of Riordan's arrays as solutions to difference equations

Asymptotic analysis of these arrays

Connection between combinatorics and difference equations

Abstract

In this paper, the describing of rational Riordan's arrays from the combinatorial analysis is represented as solutions of a Cauchy problem for two-dimensional difference equations and it is researched the asymptotic of these arrays.