On some alternative characterization of Riordan arrays

We give several new characterizations of Riordan Arrays, the most important of which is: if {d(n,k)}(n,k epsilon 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 epsilon N) is Riordan. We also provide some applications of these characterizations to the lattice path theory.