Boltzmann Oracle for Combinatorial Systems

Carine Pivoteau 1 Bruno Salvy 2 Michèle Soria 1
1 APR - Algorithmes, Programmes et Résolution
LIP6 - Laboratoire d'Informatique de Paris 6
2 ALGORITHMS - Algorithms
Inria Paris-Rocquencourt
Abstract : 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.
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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-00346845v2⟩

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