Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5773057 | Linear Algebra and its Applications | 2017 | 15 Pages |
Abstract
We first consider two groups, F0={gâC[[z]]|g(0)â 0} under multiplication and F1=zF0 under composition, where C[[z]] is the ring of formal power series over the complex field. It is known that the Riordan group R is isomorphic to the semidirect product F0âF1. It may be viewed as a group extension of F1 by F0. In this paper, the group of three-dimensional Riordan arrays is obtained from an extension of the group R by F0. This concept extends to the group of multi-dimensional Riordan arrays. As an application, we illustrate the use of the three-dimensional Riordan array in multiple combinatorial sums.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Gi-Sang Cheon, Sung-Tae Jin,