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.

Sequence characterization of Riordan arrays / T.-X. He; R. Sprugnoli. - In: DISCRETE MATHEMATICS. - ISSN 0012-365X. - STAMPA. - 309(2009), pp. 3960-3972. [10.1016/j.disc.2008.11.021]

Sequence characterization of Riordan arrays

SPRUGNOLI, RENZO
2009

Abstract

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.
309
3960
3972
T.-X. He; R. Sprugnoli
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2158/369183
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