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A Riordan group poset
- Authors
- Shapiro, Louis W.; Song, Minho
- Issue Date
- 15-May-2024
- Publisher
- Elsevier Inc.
- Keywords
- Catalan numbers; Motzkin numbers; Poset; Riordan matrix; Schröder numbers
- Citation
- Linear Algebra and Its Applications, v.689, pp 60 - 85
- Pages
- 26
- Indexed
- SCIE
SCOPUS
- Journal Title
- Linear Algebra and Its Applications
- Volume
- 689
- Start Page
- 60
- End Page
- 85
- ISSN
- 0024-3795
1873-1856
- Abstract
- In this paper, we look at Riordan arrays with nonnegative integer entries. In the set, if AT=B for a nonnegative integer matrix T, then we say A≤B. Our primary focus centers around six kinds of key arrays: Appell, Bell, two-Bell, Natural, Hankel, and Pseudo-involution. We examine relations among Hankel, Bell and two-Bell in general, while the other entries are treated case by case. We start by looking at individual cases related to the little and large Schröder numbers. Then we look at the families related to k-Catalan arrays, k-Schröder arrays, and k-Motzkin arrays. We often can give combinatorial interpretations. Along the way, several intriguing counterexamples occur. © 2024 Elsevier Inc.
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