Generating functions for generating trees

Details Generating functions for generating trees Generating functions for generating trees

2004-11-11

arxiv.org/abs/math/0411250v1

Discrete Mathematics 246 (1-3) (2002) 29-55

Mathematics

Combinatorics

This article corresponds, up to minor typo corrections, to the article submitted to Discrete Mathematics (Elsevier) in Nov. 19

Scientific paper

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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