Sequence Characterization of Riordan Arrays

Tian-Xiao He, Renzo Sprugnoli

Research output: Journal ArticleArticlepeer-review


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.

Post-print file available for download. Working title on post print: A/Z Characterization of Riordan Arrays.

Original languageAmerican English
JournalDiscrete Mathematics
StatePublished - Jun 2009


  • Riordan arrays
  • AA-sequence
  • ZZ-sequence
  • Hitting-time subgroup


  • Applied Mathematics
  • Mathematics

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