On the Central Description of the Group of Riordan Arrays

2020/07/15 by Paul Barry, Barry, Paul
Mathematics · #11C20 #20G05 #20H25 #20H25. 15A30 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Primary Primary 15A30 #Secondary 15B36

paper · pdf · doi:10.48550/arxiv.2007.07771

openalex publication_date 2020/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide an alternative description of the group of Riordan arrays, by using two power series of the form ∑_n=0^∞ g_n xⁿ, where g₀ ≠ 0 to build a typical element of the constructed group. We relate these elements to Riordan arrays in the usual description, showing that each newly constructed element is the vertical half of a "usual" element. The product rules and the construction of the inverse are given in this new description, which we call a "central" description, because of links to the central coefficients of Riordan arrays. This is done for the case of ordinary generating functions. Finally, we briefly look at the exponential case.

Related

• Centralizers of the Riordan Group
• On the inversion of Riordan arrays
• On Sums, Derivatives, and Flips of Riordan Arrays
• Riordan Groups in higher Dimensions
• On the partial sums of Riordan arrays