We use an algebraic approach to study the connection between generating trees and proper Riordan Arrays deriving a theorem that, under suitable conditions, associates a Riordan Array to a generating tree and vice versa. Thus, we can use results from the theory of Riordan Arrays to study properties of generating trees. In particular, we can find, in a general and easy way, the generating functions counting the distribution of trees' nodes at each level. The connection between Riordan Arrays and transfer matrices is also shown.

Generating trees and proper Riordan Arrays / D. MERLINI; M. VERRI. - In: DISCRETE MATHEMATICS. - ISSN 0012-365X. - STAMPA. - 218:(2000), pp. 167-183. [10.1016/S0012-365X(99)00343-X]

Generating trees and proper Riordan Arrays

MERLINI, DONATELLA;VERRI, MARIA CECILIA
2000

Abstract

We use an algebraic approach to study the connection between generating trees and proper Riordan Arrays deriving a theorem that, under suitable conditions, associates a Riordan Array to a generating tree and vice versa. Thus, we can use results from the theory of Riordan Arrays to study properties of generating trees. In particular, we can find, in a general and easy way, the generating functions counting the distribution of trees' nodes at each level. The connection between Riordan Arrays and transfer matrices is also shown.
2000
218
167
183
D. MERLINI; M. VERRI
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/309247
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