Some matrix identities on colored Motzkin paths

doi:10.1016/j.disc.2017.07.006

	Some matrix identities on colored Motzkin paths
	Yang, Sheng-Liang 1; Dong, Yan-Ni 1; He, Tian-Xiao 2
刊名	DISCRETE MATHEMATICS
	2017-12
卷号	340 期号:12 页码:3081-3091
关键词	Riordan array Catalan matrix Motzkin path Fibonacci polynomial Lucas polynomial Chebyshev polynomial
ISSN号	0012-365X
DOI	10.1016/j.disc.2017.07.006
英文摘要	Merlini and Sprugnoli (2017) give both an algebraic and a combinatorial proof for an identity proposed by Louis Shapiro by using Riordan arrays and a particular model of lattice paths. In this paper, we revisit the identity and emphasize the use of colored partial Motzkin paths as appropriate tool. By using colored Motzkin paths with weight defined according to the height of its last point, we can generalize the identity in several ways. These identities allow us to move from Fibonacci polynomials, Lucas polynomials, and Chebyshev polynomials, to the polynomials of the form (z + b)(n). (C) 2017 Elsevier B.V. All rights reserved.
资助项目	National Science Foundation of China[11561044]
WOS研究方向	Mathematics
语种	英语
出版者	ELSEVIER SCIENCE BV
WOS记录号	WOS:000412621100039
状态	已发表
内容类型	期刊论文
源URL	[http://119.78.100.223/handle/2XXMBERH/32995]
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. Some matrix identities on colored Motzkin paths[J]. DISCRETE MATHEMATICS,2017,340(12):3081-3091.
APA	Yang, Sheng-Liang,Dong, Yan-Ni,&He, Tian-Xiao.(2017).Some matrix identities on colored Motzkin paths.DISCRETE MATHEMATICS,340(12),3081-3091.
MLA	Yang, Sheng-Liang,et al."Some matrix identities on colored Motzkin paths".DISCRETE MATHEMATICS 340.12(2017):3081-3091.