A Unified Approach for the Catalan Matrices by Using Riordan Arrays

Tian-Xiao He; Yan-Ni Dong; Sheng-liang Yang; Yan-Xue Xu

doi:10.1016/j.laa.2018.07.037

A Unified Approach for the Catalan Matrices by Using Riordan Arrays

Tian-Xiao He, Yan-Ni Dong, Sheng-liang Yang, Yan-Xue Xu

Illinois Wesleyan University

Research output: Journal Article › Article › peer-review

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.

Original language	American English
Journal	Linear Algebra and Its Applications
Volume	558
DOIs	https://doi.org/10.1016/j.laa.2018.07.037
State	Published - Dec 2018

Disciplines

Physical Sciences and Mathematics
Mathematics

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10.1016/j.laa.2018.07.037License: Unspecified

Cite this

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title = "A Unified Approach for the Catalan Matrices by Using Riordan Arrays",

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.",

author = "Tian-Xiao He and Yan-Ni Dong and Sheng-liang Yang and Yan-Xue Xu",

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AU - Xu, Yan-Xue

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AB - 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.

UR - https://www.sciencedirect.com/science/article/pii/S002437951830377X#bfn0010

U2 - 10.1016/j.laa.2018.07.037

DO - 10.1016/j.laa.2018.07.037

M3 - Article

VL - 558

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

A Unified Approach for the Catalan Matrices by Using Riordan Arrays

Abstract

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