The three 'R's and Dual Riordan Arrays

2016/09/05 by Thomas M. Richardson, Richardson, Thomas M.
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1609.01193

openalex publication_date 2016/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe how the reversion of a series is related to convolutional recurrence relations for the series, and we place this relationship in the context of Riordan arrays. As an example of the approach, we give new recurrence relations for the sequences of Patalan numbers. We also consider the concepts of recursive matrices and dual Riordan arrays, and their application to previous work on the super Patalan numbers.

Citations

• Some Open Questions about Random Walks, Involutions, Limiting Distributions, and Generating Functions

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