Boltzmann Oracle for Combinatorial Systems

Carine Pivoteau (1) , Bruno Salvy (2) , Michèle Soria (1)

1 LIP6 - Laboratoire d'Informatique de Paris 6
2 ALGORITHMS - Algorithms

Boltzmann random generation applies to well-defined systems of recursive combinatorial equations. It relies on oracles giving values of the enumeration generating series inside their disk of convergence. We show that the combinatorial systems translate into numerical iteration schemes that provide such oracles. In particular, we give a fast oracle based on Newton iteration.

Mots clés: Random generation; Boltzmann generation; combinatorics; Newton iteration

Domaines: Combinatoire [math.CO]; Algorithme et structure de données [cs.DS]

Carine Pivoteau, Bruno Salvy, Michèle Soria. Boltzmann Oracle for Combinatorial Systems. Fifth Colloquium on Mathematics and Computer Science, Sep 2008, Blaubeuren, Germany. pp.475-488. ⟨hal-00346845v1⟩