Proper generating trees and their internal path length

Authors:
Donatella Merlini
Affiliations:
Dipartimento di Sistemi e Informatica, viale Morgagni 65, 50134, Firenze, Italy
Venue:
Discrete Applied Mathematics
Year:
2008

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Abstract

We find the generating function counting the total internal path length of any proper generating tree. This function is expressed in terms of the functions (d(t),h(t)) defining the associated proper Riordan array. This result is important in the theory of Riordan arrays and has several combinatorial interpretations.