The author defines ℓ-level almost-Riordan arrays, states without proof that they form a group, and gives sequence and compression characterizations that reduce to previously published equations.
The Triple Riordan Group
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abstract
We define the triple Riordan group, whose elements consist of $4$-tuples of power series $(g, f_1, f_2, f_3)$ with $g\in \mathbf{R}[[x^3]]$, and $f_1, f_2, f_3 \in x\mathbf{R}[[x^3]]$, for an appropriate ring $\mathbf{R}$. The construction of this group generalizes that of the double Riordan group, and lays the pattern for further generalizations.
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Sequence Characterization of Multiple Almost-Riordan Arrays and Their Compressions
The author defines ℓ-level almost-Riordan arrays, states without proof that they form a group, and gives sequence and compression characterizations that reduce to previously published equations.