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Article
A Unified Approach for the Catalan Matrices by Using Riordan Arrays
Linear Algebra and its Applications
(2018)
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.
Disciplines
Publication Date
Winter December, 2018
DOI
https://doi.org/10.1016/j.laa.2018.07.037
Publisher Statement
Linear Algebra and its Applications is published by Elsevier. For more information visit the journal homepage.
Citation Information
Tian-Xiao He, Yan-Ni Dong, Sheng-liang Yang and Yan-Xue Xu. "A Unified Approach for the Catalan Matrices by Using Riordan Arrays" Linear Algebra and its Applications Vol. 558 (2018) p. 25 - 43 ISSN: 0024-3795 Available at: http://works.bepress.com/tian_xiao_he/89/