Generating tuples of integers modulo the action of a permutation group and applications

Nicolas Borie (1)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge

Originally motivated by algebraic invariant theory, we present an algorithm to enumerate integer vectors modulo the action of a permutation group. This problem generalizes the generation of unlabeled graph up to an isomorphism. In this paper, we present the full development of a generation engine by describing the related theory, establishing a mathematical and practical complexity, and exposing some benchmarks. We next show two applications to e ective invariant theory and e ective Galois theory.

Mots clés: Énumération à un isomorphisme près; Combinatoire énumérative; Théorie effective des invariants; Théorie de Galois effective

Domaines: Combinatoire [math.CO]

Nicolas Borie. Generating tuples of integers modulo the action of a permutation group and applications. FPSAC 2013, Jun 2013, Paris, France. pp.797-808. ⟨hal-00823212⟩