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.
On the Group of Almost-Riordan Arrays
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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.
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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.