Sequence Characterization of Riordan Arrays
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.
Tian-Xiao He. "Sequence Characterization of Riordan Arrays" Discrete Mathematics 309 (2009): 3962-3974.
Available at: http://works.bepress.com/tian_xiao_he/3
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