| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 8953094 | Linear Algebra and its Applications | 2018 | 21 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Sheng-Liang Yang, Yan-Ni Dong, Tian-Xiao He, Yan-Xue Xu,