Generation modulo the action of a permutation group

Abstract

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 effective invariant theory and effective Galois theory.

Keywords

• generation up to an isomorphism
• enumerative combinatorics
• computational invariant theory
• effective galois theory
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]