1. Generation modulo the action of a permutation group
- Author
-
Nicolas Borie
- Subjects
generation up to an isomorphism ,enumerative combinatorics ,computational invariant theory ,effective galois theory ,[info.info-dm] computer science [cs]/discrete mathematics [cs.dm] ,Mathematics ,QA1-939 - 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.
- Published
- 2013
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