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Sequence characterization of Riordan arrays

2008; Elsevier BV; Volume: 309; Issue: 12 Linguagem: Inglês

10.1016/j.disc.2008.11.021

1872-681X

Tian-Xiao He, Renzo Sprugnoli,

Genome Rearrangement Algorithms

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.