The Double Almost-Riordan Arrays and Their Sequence Characterization, Compression, and Total Positivity

TL;DR

This paper introduces double almost-Riordan arrays, explores their algebraic structure, sequence properties, compression methods, and criteria for total positivity, expanding the theoretical framework of Riordan array generalizations.

Contribution

It defines the double almost-Riordan arrays, establishes their group structure, and investigates their sequence characteristics, compression, and total positivity criteria.

Findings

Double almost-Riordan arrays form a mathematical group.

Production matrices for these arrays are derived.

Criteria for total positivity of the arrays are established.

Abstract

In this paper, we define double almost-Riordan arrays and find that the set of all double almost-Riordan arrays forms a group, called the double almost-Riordan group. We also obtain the sequence characteristics of double almost-Riordan arrays and give the production matrices for double almost-Riordan arrays. We define the compression of double almost-Riordan arrays and present their sequence characterization. Finally we give a characteristic for the total positivity of double Riordan arrays, by using which we discuss the total positivity for compressed double almost-Riordan arrays.