Generating functions for generating trees

Authors:
Cyril Banderier;Mireille Bousquet-Mélou;Alain Denise;Philippe Flajolet;Danièle Gardy;Dominique Gouyou-Beauchamps
Affiliations:
Projet Algorithmes, INRIA Rocquencourt, F-78153 Le Chesnay, France;CNRS, LaBRI, Université Bordeaux 1, 351 cours de la Libération, F-33405 Talence Cedex, France;LRI, Bâtiment 490, Université Paris-Sud XI, F-91405 Orsay Cedex, France;Projet Algorithmes, INRIA Rocquencourt, F-78153 Le Chesnay, France;Université de Versailles/Saint-Quentin, Laboratoire PRISM, 45, avenue des États-Unis, F-78035 Versailles Cedex, France;LRI, Bâtiment 490, Université Paris-Sud XI, F-91405 Orsay Cedex, France
Venue:
Discrete Mathematics
Year:
2002

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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.