A unified approach for the Catalan matrices by using Riordan arrays
| Autor: | Tian-Xiao He, Yan-Ni Dong, Sheng-Liang Yang, Yan-Xue Xu |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Discrete mathematics
Numerical Analysis Mathematics::Combinatorics Algebra and Number Theory Combinatorial interpretation 010102 general mathematics 0102 computer and information sciences Convolution of probability distributions 01 natural sciences language.human_language Catalan number 010201 computation theory & mathematics language Discrete Mathematics and Combinatorics Catalan Geometry and Topology 0101 mathematics Mathematics |
| Zdroj: | Linear Algebra and its Applications. 558:25-43 |
| ISSN: | 0024-3795 |
| Popis: | We study generalized Catalan matrices based on the Riordan array and Fuss–Catalan numbers. A unified combinatorial interpretation for the entries of the generalized Catalan matrices is presented by means of m-Dyck paths. Some properties and examples of the generalized Catalan matrices are given including a new convolution formula for the generalized Catalan numbers. Finally, we present applications of generalized Catalan matrices to the problems in counting the hill-free and lower peak-free m-Dyck paths. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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