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.
Proper generating trees and their internal path length / D. MERLINI. - In: DISCRETE APPLIED MATHEMATICS. - ISSN 0166-218X. - STAMPA. - 156 (5):(2008), pp. 627-646. [10.1016/j.dam.2007.08.051]
Proper generating trees and their internal path length
MERLINI, DONATELLA
2008
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.
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