The m-Schroder paths and m-Schroder numbers

doi:10.1016/j.disc.2020.112209

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	The m-Schroder paths and m-Schroder numbers
	Yang, Sheng-Liang; Jiang, Mei-yang
刊名	DISCRETE MATHEMATICS
	2021-02
卷号	344 期号:2 页码:-
关键词	Riordan array m-Dyck path m-Schroder path m-Schroder number m-Schroder matrix Generating function
ISSN号	0012-365X
DOI	10.1016/j.disc.2020.112209
英文摘要	In this paper, we introduce a variant of the m-Schroder paths, i.e. of those lattice paths from (0, 0) to (mn, 0) with up steps U = (1, 1), down steps D-(m) = (1, 1 - m) and horizontal-down steps H-(m) = (2, 2-m), which never go below the x-axis. The number of m-Schroder paths of length mn is called the nth m-Schroder number, while the number of m-Schroder paths of length mn with no horizontal-down steps ending on the x-axis is called nth small m-Schroder number. We present two types of generalization of Schroder matrices. The entries are interpreted in terms of the number of partial m-Schroder paths. Then we show that these matrices are Riordan arrays, and we give some properties from this result. In particular, we obtain that the nth m-Schroder number is twice of the nth small m-Schroder number for n >= 1, and we show that the A-sequence of the m-Schroder matrix is the sequence of the (m - 1)-Schroder numbers. Finally, we study other two m-Schroder matrices whose row sums are the m-Schroder numbers and small m-Schroder numbers respectively. (c) 2020 Elsevier B.V. All rights reserved.
WOS研究方向	Mathematics
语种	英语
出版者	ELSEVIER
WOS记录号	WOS:000598172000028
内容类型	期刊论文
源URL	[http://ir.lut.edu.cn/handle/2XXMBERH/147311]
专题	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,Jiang, Mei-yang. The m-Schroder paths and m-Schroder numbers[J]. DISCRETE MATHEMATICS,2021,344(2):-.
APA	Yang, Sheng-Liang,&Jiang, Mei-yang.(2021).The m-Schroder paths and m-Schroder numbers.DISCRETE MATHEMATICS,344(2),-.
MLA	Yang, Sheng-Liang,et al."The m-Schroder paths and m-Schroder numbers".DISCRETE MATHEMATICS 344.2(2021):-.