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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.