2022/10/05 by Caroline Bang, Bang, Caroline, Matias von Bell +11
Arts and Humanities · Social Sciences · #Combinatorics (math.CO) #FOS: Mathematics #Language, Linguistics, Cultural Analysis #Linguistic Variation and Morphology #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2210.02566
openalex publication_date 2022/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study three operations on Riordan arrays. First, we investigate when the sum of Riordan arrays yields another Riordan array. We characterize the A- and Z-sequences of these sums of Riordan arrays, and also identify an analog for A-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.