On the Group of Almost-Riordan Arrays

2016/06/16 by Paul Barry, Barry, Paul · 3 citations
Mathematics · Medicine · #Advanced Combinatorial Mathematics #Cell Adhesion Molecules Research

paper · pdf · doi:10.48550/arxiv.1606.05077

Abstract

We study a super group of the group of Riordan arrays, where the elements of the group are given by a triple of power series. We show that certain subsets are subgroups, and we identify a normal subgroup whose cosets correspond to Riordan arrays. We give an example of an almost-Riordan array that has been studied in the context of Hankel and Hankel plus Toepliz matrices, and we show that suitably chosen almost-Riordan arrays can lead to transformations that have interesting Hankel transform properties.

Citations

• Production Matrices and Riordan Arrays

Cited by

• On a Central Transform of Integer Sequences
• Sequence Characterization of Multiple Almost-Riordan Arrays and Their Compressions
• Chebyshev moments and Riordan involutions

Related

• Riordan Groups in higher Dimensions
• On pseudo-involutions, involutions and quasi-involutions in the group of almost Riordan arrays
• Multiple almost-Riordan arrays and the multiple almost-Riordan group
• The Double Almost-Riordan Arrays and Their Sequence Characterization, Compression, and Total Positivity
• On the inversion of Riordan arrays