Generating functions for generating trees
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.
Keywords
Cite
@article{arxiv.math/0411250,
title = {Generating functions for generating trees},
author = {Cyril Banderier and Philippe Flajolet and Daniele Gardy and Mireille Bousquet-Melou and Alain Denise and Dominique Gouyou-Beauchamps},
journal= {arXiv preprint arXiv:math/0411250},
year = {2014}
}
Comments
This article corresponds, up to minor typo corrections, to the article submitted to Discrete Mathematics (Elsevier) in Nov. 1999, and published in its vol. 246(1-3), March 2002, pp. 29-55