An evaluation approach to computing invariants rings of permutation groups

2011/10/17 by Nicolas Borie, Borie, Nicolas, Nicolas M. Thiéry +1 · 1 citation
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #graph theory and CDMA systems #math.CO

paper · pdf · doi:10.48550/arxiv.1110.3849

18 pages, 4 figures, In Proceedings of MEGA 2011, March 2011

arxiv created 2011/10/17 · openalex publication_date 2011/10/17 · arxiv updated 2011/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using evaluation at appropriately chosen points, we propose a Gröbner basis free approach for calculating the secondary invariants of a finite permutation group. This approach allows for exploiting the symmetries to confine the calculations into a smaller quotient space, which gives a tighter control on the algorithmic complexity, especially for large groups. This is confirmed by extensive benchmarks using a Sage implementation.

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

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