$A$-sequences, $Z$-sequence, and $B$-sequences of Riordan Matrices

TL;DR

This paper introduces new sequence characterizations ($A$, $Z$, and $B$-sequences) for Riordan matrices, explores their subgroup structures, and applies these concepts to RNA matrices and Pascal-like Riordan matrices.

Contribution

It presents novel $B$-sequences for Riordan arrays and characterizes Riordan matrices with two $B$-sequences, expanding understanding of their algebraic structure.

Findings

Characterization of Riordan matrices with two $B$-sequences

Application to RNA type matrices

Analysis of $A$-, $Z$-, and $B$-sequences of Pascal-like matrices

Abstract

We defined two type $B$-sequences of Riordan arrays and present the $A$-sequence characterization and $Z$-sequence characterization of the Riordan matrices with two type $B$-sequences. The subgroups characterized by $A$-sequences and $Z$-sequences are studied. The application of the sequence characterization to the RNA type matrices is discussed. Finally, we investigate the $A$-, $Z$-, and $B$-sequences of the Pascal like Riordan matrices.