The three 'R's and Dual Riordan Arrays
Thomas M. Richardson
TL;DR
This paper explores the relationship between series reversion, convolutional recurrence relations, and Riordan arrays, introducing new recurrences for Patalan numbers and discussing recursive matrices and dual Riordan arrays.
Contribution
It presents a novel connection between series reversion and Riordan arrays, and introduces new recurrence relations for Patalan numbers and super Patalan numbers.
Findings
New recurrence relations for Patalan numbers
Relationship between series reversion and Riordan arrays
Application to super Patalan numbers
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Mathematical Identities · semigroups and automata theory