Generalized Riordan Groups and Operators on Polynomials

Abstract

We present an approach to generalized Riordan arrays which is based on operations in one large group of lower triangular matrices. This allows for direct proofs of many properties of weighted Sheffer sequences, and shows that all the groups arising from different weights are isomorphic since they are conjugate. We also prove a result about the intersection of two generalized Riordan with different weights.