Diagonals in Riordan matrices and applications

TL;DR

This paper presents a new diagonal-based structural method for Riordan matrices, offering insights into their properties and applications, including characterizing palindromic Riordan polynomials with combinatorial interpretations.

Contribution

It introduces a diagonal recurrence relation approach for Riordan matrices, complementing existing descriptions and enabling new combinatorial characterizations.

Findings

New diagonal recurrence relations for Riordan matrices

Characterization of palindromic Riordan polynomials

Combinatorial interpretation via lattice paths

Abstract

We introduce a method for describing Riordan matrices via recurrence relations along their diagonals. This provides a new structural description that complements the classical row-wise and column-wise constructions via the A-sequence. As an application, we characterize families of palindromic Riordan polynomials, yielding a new combinatorial interpretation in terms of lattice paths.