Generating tuples of integers modulo the action of a permutation group and applications
arXiv:1211.6261
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.
12 pages, 1 figures, 3 graphics, 2 algorithms, 3 tables. Submitted as extended abstract to FPSAC 2013