A Symbolic Treatment of Riordan Arrays
Combinatorics
2015-05-28 v1
Abstract
We approach Riordan arrays and their generalizations via umbral symbolic methods. This new approach allows us to derive fundamental aspects of the theory of Riordan arrays as immediate consequences of the umbral version of the classical Abel's identity for polynomials. In particular, we obtain a novel non-recursive formula for Riordan arrays and derive, from this new formula, some known recurrences and a new recurrence relation for Riordan arrays.
Keywords
Cite
@article{arxiv.1505.07253,
title = {A Symbolic Treatment of Riordan Arrays},
author = {José Agapito and Ângela Mestre and Pasquale Petrullo and Maria M. Torres},
journal= {arXiv preprint arXiv:1505.07253},
year = {2015}
}
Comments
16 pages