Riordan arrays, Lukasiewicz paths and Narayana polynomials

doi:10.1016/j.laa.2021.03.012

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	Riordan arrays, Lukasiewicz paths and Narayana polynomials
	Yang, Lin; Yang, Sheng-Liang
刊名	LINEAR ALGEBRA AND ITS APPLICATIONS
	2021
卷号	622 页码:1-18
关键词	Riordan arrays Lukasiewicz paths Schroder paths Motzkin paths Narayana numbers Narayana polynomials
ISSN号	0024-3795
DOI	10.1016/j.laa.2021.03.012
英文摘要	By counting weighted Lukasiewicz paths and weighted Schroder paths, we obtain two Riordan arrays in which the bivariate Narayana polynomials occur in their first columns. We present a bijection between the weighted Lukasiewicz paths and the weighted Schroder paths, hence we obtain a new combinatorial interpretation for Schroder numbers: the nth Schroder number equals the number of Lukasiewicz paths of length n in which all up steps are weighted by 1, and other steps are weighted by 2. Furthermore, we provide some identities on the bivariate Narayana polynomials by considering two Riordan arrays related to weighted Motzkin paths. (c) 2021 Elsevier Inc. All rights reserved.
WOS研究方向	Mathematics
语种	英语
出版者	ELSEVIER SCIENCE INC
WOS记录号	WOS:000646198400001
内容类型	期刊论文
源URL	[http://ir.lut.edu.cn/handle/2XXMBERH/148175]
专题	理学院
作者单位	Lanzhou Univ Technol, Dept Appl Math, Lanzhou 730050, Gansu, Peoples R China
推荐引用方式 GB/T 7714	Yang, Lin,Yang, Sheng-Liang. Riordan arrays, Lukasiewicz paths and Narayana polynomials[J]. LINEAR ALGEBRA AND ITS APPLICATIONS,2021,622:1-18.
APA	Yang, Lin,&Yang, Sheng-Liang.(2021).Riordan arrays, Lukasiewicz paths and Narayana polynomials.LINEAR ALGEBRA AND ITS APPLICATIONS,622,1-18.
MLA	Yang, Lin,et al."Riordan arrays, Lukasiewicz paths and Narayana polynomials".LINEAR ALGEBRA AND ITS APPLICATIONS 622(2021):1-18.