On some alternative characterizations of Riordan arrays

http://dx.doi.org/10.4153/CJM-1997-015-x
Canad. J. Math. 49(1997), 301-320

  Published:1997-04-01
 Printed: Apr 1997

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.