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Level generating trees and proper Riordan arrays

Baccherini D. (Universit'a di Firenze, Dipartimento di Sistemi e Informatica, Firenze, Italy)
Merlini D. (Universit'a di Firenze, Dipartimento di Sistemi e Informatica, Firenze, Italy)
Sprugnoli R. (Universit'a di Firenze, Dipartimento di Sistemi e Informatica, Firenze, Italy)

We introduce a generalization of generating trees named Level Generating Trees and study the connection between these structures and proper Riordan arrays, deriving a theorem that, under suitable conditions, associates a Riordan array to a Level Generating Tree and vice versa. We illustrate our main results by several examples concerning classical combinatorial structures.

Keywords: Riordan arrays, generating trees, generating functions