## 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.

Original language | American English |
---|---|

Journal | Discrete Mathematics |

Volume | 309 |

State | Published - Jun 2009 |

## Keywords

- Riordan arrays
- AA-sequence
- ZZ-sequence
- Hitting-time subgroup

## Disciplines

- Applied Mathematics
- Mathematics