On Some Alternative Characterizations of Riordan Arrays

Abstract We give several new characterizations of Riordan Arrays, the most important of which is: if { d n,k } n,k ∈ N is a lower triangular arraywhose 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 ∈ N is Riordan. We also provide some applications of these characterizations to the lattice path theory.