Interesting Esoterica

Generating functions for generating trees

Article by Cyril Banderier and Mireille Bousquet-Mélou and Alain Denise and Philippe Flajolet and Danièle Gardy and Dominique Gouyou-Beauchamps
  • Published in 2002
  • Added on
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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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BibTeX entry

@article{Generatingfunctionsforgeneratingtrees,
	title = {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.},
	url = {https://www.sciencedirect.com/science/article/abs/pii/S0012365X01002503},
	year = 2002,
	author = {Cyril Banderier and Mireille Bousquet-M{\'{e}}lou and Alain Denise and Philippe Flajolet and Danièle Gardy and Dominique Gouyou-Beauchamps},
	comment = {},
	urldate = {2020-10-24},
	collections = {integerology}
}