Article
(m, r)-CENTRAL RIORDAN ARRAYS AND THEIR APPLICATIONS
Czechoslovak Mathematical Journal
(2017)
Abstract
Excerpt from the abstract:
It is known that the (m, r)-central coefficient triangles of any Riordan array are also Riordan arrays. In this paper, for a Riordan array G = (d, h) with h(0) = 0 and d(0), h′(0) 6≠ 0, we obtain the generating function of its (m, r)-central coefficients and give an explicit representation for the (m, r)-central Riordan array G(m,r)in terms of the Riordan array G. Meanwhile, the algebraic structures of the (m, r)-central Riordan arrays are also investigated, such as their decompositions, their inverses, and their recessive expressions in terms of m and r. As applications, we determine the (m, r)-central Riordan arrays of the Pascal matrix and other Riordan arrays, from which numerous identities are constructed by a uniform approach.
Keywords
- Riordan array,
- central coefficient,
- central Riordan array,
- generating function,
- Fuss-Catalan number,
- Pascal matrix,
- Catalan matrix
Disciplines
Publication Date
Fall October, 2017
DOI
https://doi.org/10.21136/CMJ.2017.0165-16
Publisher Statement
The Czechoslovak Mathematical Journal is published by Institute of Mathematics, Czech Academy of Sciences and distributed by Springer, and is posted here with permission. For more information on this publication please see the journal homepage.
Citation Information
Tian-Xiao He, Sheng-liang Yang and Yan-Xue Xu. "(m, r)-CENTRAL RIORDAN ARRAYS AND THEIR APPLICATIONS" Czechoslovak Mathematical Journal Vol. 67 Iss. 4 (2017) p. 919 - 936 ISSN: 0011-4642 Available at: http://works.bepress.com/tian_xiao_he/83/