The aim of this text is to introduce the beginner to the theory of Riordan arrays. Starting in a
simple and constructive manner, the basic structure of these arrays is explained with clear …

We translate the concept of succession rule and the ECO method into matrix notation,
introducing the concept of production matrix. This allows us to combine our method with …

We define an infinite sequence of generalizations, parametrized by an integer $ m\ge 1$, of
the Stieltjes–Rogers and Thron–Rogers polynomials; they arise as the power-series …

In this paper, we define double almost-Riordan arrays and find that the set of all double
almost-Riordan arrays forms a group, called the double almost-Riordan group. We also …

We determine which (ordinary) Riordan arrays are the coefficient arrays of a family of
orthogonal polynomials. In so doing, we are led to introduce a family of polynomials, which …

We introduce a triangular array $\widehat {\sf L}^{(\alpha)} $ of 5-variable homogeneous
polynomials that enumerate Laguerre digraphs (digraphs in which each vertex has out …

In Deepak Dhar's model of abelian distributed processors, automata occupy the vertices of a
graph and communicate via the edges. We show that two simple axioms ensure that the final …

We introduce the generic Lah polynomials L n, k (ϕ), which enumerate unordered forests of
increasing ordered trees with a weight ϕ i for each vertex with i children. We show that, if the …

The main objects of the investigation presented in this paper are branched-continued-
fraction representations of ratios of contiguous hypergeometric series and type II multiple …

We study involutions in the Riordan group, especially those with combinatorial meaning. We
give a new determinantal criterion for a matrix to be a Riordan involution and examine …