Self-inverse Sheffer sequences and Riordan involutions

TL;DR

This paper characterizes all involutions in the Riordan group by translating existing results on self-inverse Sheffer sequences, providing a comprehensive understanding of their structure and properties.

Contribution

It offers a complete description of Riordan group involutions through the lens of self-inverse Sheffer sequences, connecting two mathematical concepts.

Findings

All Riordan group involutions are characterized via self-inverse Sheffer sequences.

The paper translates Brown and Kuczma's results to the context of Riordan involutions.

Provides a unified framework linking Sheffer sequences and Riordan group involutions.

Abstract

In this short note we focus on self-inverse Sheffer sequences and involutions in the Riordan group. We translate the results of Brown and Kuczma on self-inverse sequences of Sheffer polynomials to describe all involutions in the Riordan group.