On Sums, Derivatives, and Flips of Riordan Arrays
Combinatorics
2025-09-09 v1 Rings and Algebras
Abstract
We study three operations on Riordan arrays. First, we investigate when the sum of Riordan arrays yields another Riordan array. We characterize the - and -sequences of these sums of Riordan arrays, and also identify an analog for -sequences when the sum of Riordan arrays does not yield a Riordan array. In addition, we define the new operations `Der' and `Flip' on Riordan arrays. We fully characterize the Riordan arrays resulting from these operations applied to the Appell and Lagrange subgroups of the Riordan group. Finally, we study the application of these operations to various known Riordan arrays, generating many combinatorial identities in the process.
Keywords
Cite
@article{arxiv.2210.02566,
title = {On Sums, Derivatives, and Flips of Riordan Arrays},
author = {Caroline Bang and Matias von Bell and Eric Culver and Jessica Dickson and Stoyan Dimitrov and Rachel Perrier and Sheila Sundaram},
journal= {arXiv preprint arXiv:2210.02566},
year = {2025}
}
Comments
35 pages