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On some alternative characterizations of Riordan arrays

  Published:1997-04-01
 Printed: Apr 1997
  • Donatella Merlini
  • Douglas G. Rogers
  • Renzo Sprugnoli
  • M. Cecilia Verri
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Abstract

We give several new characterizations of Riordan Arrays, the most important of which is: if $\{d_{n,k}\}_{n,k \in {\bf N}}$ is a lower triangular array whose generic element $d_{n,k}$ linearly depends on the elements in a well-defined though large area of the array, then $\{d_{n,k}\}_{n,k \in {\bf N}}$ is Riordan. We also provide some applications of these characterizations to the lattice path theory.
MSC Classifications: 05A15, 05C38 show english descriptions Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx]
Paths and cycles [See also 90B10]
05A15 - Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx]
05C38 - Paths and cycles [See also 90B10]
 

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