Generating functions for generating trees

Cyril Banderier 1, 2, * Philippe Flajolet 2 Danièle Gardy 3 Mireille Bousquet-Mélou 4 Alain Denise 5 Dominique Gouyou-Beauchamps 5
* Corresponding author
2 ALGO - Algorithms
Inria Paris-Rocquencourt
3 SMIS - Secured and Mobile Information Systems
PRISM - Parallélisme, Réseaux, Systèmes, Modélisation, UVSQ - Université de Versailles Saint-Quentin-en-Yvelines, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR8144
Abstract : Certain families of combinatorial objects admit recursive descriptions in terms of generating trees: each node of the tree corresponds to an object, and the branch leading to the node encodes the choices made in the construction of the object. Generating trees lead to a fast computation of enumeration sequences (sometimes, to explicit formulae as well) and provide efficient random generation algorithms. We investigate the links between the structural properties of the rewriting rules defining such trees and the rationality, algebraicity, or transcendence of the corresponding generating function.
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Submitted on : Wednesday, November 10, 2004 - 8:08:54 PM
Last modification on : Thursday, February 7, 2019 - 5:53:11 PM
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Cyril Banderier, Philippe Flajolet, Danièle Gardy, Mireille Bousquet-Mélou, Alain Denise, et al.. Generating functions for generating trees. Discrete Mathematics, Elsevier, 2002, 246 (1-3), pp.29-55. ⟨hal-00003258⟩

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