A unified approach for the Catalan matrices by using Riordan arrays

doi:10.1016/j.laa.2018.07.037

	A unified approach for the Catalan matrices by using Riordan arrays
	Yang, Sheng-Liang 1; Dong, Yan-Ni 1; He, Tian-Xiao 2; Xu, Yan-Xue 1
刊名	LINEAR ALGEBRA AND ITS APPLICATIONS
	2018-12
卷号	558 页码:25-43
关键词	Generalized Catalan matrix Riordan array m-Dyck path Generalized binomial series Fuss-Catalan number Generating function
ISSN号	0024-3795
DOI	10.1016/j.laa.2018.07.037
英文摘要	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. (C) 2018 Elsevier Inc. All rights reserved.
资助项目	National Natural Science Foundation of China[11561044]
WOS研究方向	Mathematics
语种	英语
出版者	ELSEVIER SCIENCE INC
WOS记录号	WOS:000447075900002
状态	已发表
内容类型	期刊论文
源URL	[http://119.78.100.223/handle/2XXMBERH/32293]
专题	材料科学与工程学院理学院
通讯作者	Yang, Sheng-Liang
作者单位	1.Lanzhou Univ Technol, Dept Appl Math, Lanzhou 730050, Gansu, Peoples R China 2.Illinois Wesleyan Univ, Dept Math, Bloomington, IL 61702 USA
推荐引用方式 GB/T 7714	Yang, Sheng-Liang,Dong, Yan-Ni,He, Tian-Xiao,et al. A unified approach for the Catalan matrices by using Riordan arrays[J]. LINEAR ALGEBRA AND ITS APPLICATIONS,2018,558:25-43.
APA	Yang, Sheng-Liang,Dong, Yan-Ni,He, Tian-Xiao,&Xu, Yan-Xue.(2018).A unified approach for the Catalan matrices by using Riordan arrays.LINEAR ALGEBRA AND ITS APPLICATIONS,558,25-43.
MLA	Yang, Sheng-Liang,et al."A unified approach for the Catalan matrices by using Riordan arrays".LINEAR ALGEBRA AND ITS APPLICATIONS 558(2018):25-43.