On the half of a Riordan array

	On the half of a Riordan array
	Yang, Sheng-Liang; Xu, Yan-Xue; Gao, Xiao
刊名	ARS COMBINATORIA
	2017-07
卷号	133 页码:407-422
关键词	Riordan array central coefficient Catalan number Generating function generalized binomial series
ISSN号	0381-7032
英文摘要	The half of an infinite lower triangular matrix G = (g(n,k))(n,k >= 0) is defined to be the infinite lower triangular matrix G((1)) = (g(n,k)((1)))(n,k >= 0) such that g(n,k)((1)) = g(2n-k,n) for all n >= k >= 0. In this paper, we will show that if G is a Riordan array then its half G((1)) is also a Riordan array. We use Lagrange inversion theorem to characterize the generating functions of G((1)) in terms of the generating functions of G. Consequently, a tight relation between G((1)) and the initial array G is given, hence it is possible to invert the process and rebuild the original Riordan array G from the array G((1)). If the process of taking half of a Riordan array G is iterated r times, then we obtain a Riordan array G((r)). The further relation between the result array G((r)) and the initial array G is also considered. Some examples and applications are presented.
资助项目	National Natural Science Foundation of China[11561044]
WOS研究方向	Mathematics
语种	英语
出版者	CHARLES BABBAGE RES CTR
WOS记录号	WOS:000404082800031
状态	已发表
内容类型	期刊论文
源URL	[http://119.78.100.223/handle/2XXMBERH/33206]
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	Lanzhou Univ Technol, Dept Appl Math, Lanzhou 730050, Gansu, Peoples R China
推荐引用方式 GB/T 7714	Yang, Sheng-Liang,Xu, Yan-Xue,Gao, Xiao. On the half of a Riordan array[J]. ARS COMBINATORIA,2017,133:407-422.
APA	Yang, Sheng-Liang,Xu, Yan-Xue,&Gao, Xiao.(2017).On the half of a Riordan array.ARS COMBINATORIA,133,407-422.
MLA	Yang, Sheng-Liang,et al."On the half of a Riordan array".ARS COMBINATORIA 133(2017):407-422.