Boltzmann Oracle for Combinatorial Systems

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.

Keywords

• random generation
• boltzmann generation
• combinatorics
• newton iteration
• [math.math-co] mathematics [math]/combinatorics [math.co]
• [info.info-ds] computer science [cs]/data structures and algorithms [cs.ds]