1. Sequence characterization of Riordan arrays
- Author
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He, Tian-Xiao and Sprugnoli, Renzo
- Subjects
- *
MATHEMATICAL sequences , *GENERATING functions , *GROUP theory , *MATHEMATICAL analysis , *COMBINATORICS - Abstract
Abstract: In the realm of the Riordan group, we consider the characterization of Riordan arrays by means of the - and -sequences. It corresponds to a horizontal construction of a Riordan array, whereas the traditional approach is through column generating functions. We show how the - and -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. [Copyright &y& Elsevier]
- Published
- 2009
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