LEVEL GENERATING TREES AND PROPER RIORDAN ARRAYS

We introduce a generalization of generating trees named LevelGenerating Trees and study the connection between these structuresand proper {sc Riordan} arrays, deriving a theorem that, under suitableconditions, associates a {sc Riordan} array to a Level Generating Treeand vice versa. We illustrate our main results by several examplesconcerning classical combinatorial structures.