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

2012/11/27 by Nicolas Borie, Borie, Nicolas
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1211.6261

openalex publication_date 2012/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• An evaluation approach to computing invariants rings of permutation groups

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