Paper detail

On the Central Description of the Group of Riordan Arrays

We provide an alternative description of the group of Riordan arrays, by using two power series of the form $\sum_{n=0}^{\infty} g_n x^n$, where $g_0 \ne 0$ to build a typical element of the constructed group. We relate these elements to Riordan arrays in the usual description, showing that each newly constructed element is the vertical half of a "usual" element. The product rules and the construction of the inverse are given in this new description, which we call a "central" description, because of links to the central coefficients of Riordan arrays. This is done for the case of ordinary generating functions. Finally, we briefly look at the exponential case.