#### Abstract

In the realm of the Riordan group, we consider the characterization of Riordan arrays by means of the A- and Z-sequences. It corresponds to a horizontal construction of a Riordan array, whereas the traditional approach is through column generating functions. We show how the A- and Z-sequences of the product of two Riordan arrays are derived from those of the two factors; similar results are obtained for the inverse. We also show how the sequence characterization is applied to construct easily a Riordan array. Finally, we give the characterizations relative to some subgroups of the Riordan group, in particular, of the hitting-time subgroup. Post-print file available for download. Working title on post print: A/Z Characterization of Riordan Arrays.

#### Disciplines

Applied Mathematics | Mathematics

#### Recommended Citation

He, Tian-Xiao and Sprugnoli, Renzo, "Sequence Characterization of Riordan Arrays" (2009). *Scholarship*. 33.

https://digitalcommons.iwu.edu/math_scholarship/33

## Comments

Discrete Mathematicsis published by Elsevier, http://www.journals.elsevier.com/discrete-mathematics/.