Sequence characterization of Riordan arrays. (English) Zbl 1228.05014

Summary: In the realm of the Riordan group, we consider the characterization of Riordan arrays by means of the \(A\)- and \(Z\)-sequences. It corresponds to a horizontal construction of a Riordan array, whereas the traditional approach is through column generating functions. We show how the \(A\)- and \(Z\)-sequences of the product of two Riordan arrays are derived from those of the two factors; similar results are obtained for the inverse. We also show how the sequence characterization is applied to construct easily a Riordan array. Finally, we give the characterizations relative to some subgroups of the Riordan group, in particular, of the hitting-time subgroup.


05A05 Permutations, words, matrices


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