Effective Invariant Theory of Permutation Groups using Representation Theory

TL;DR

This paper introduces an algorithm leveraging symmetric group representation theory to efficiently compute permutation group invariants, reducing linear algebra computations and utilizing a simplified combinatorial framework.

Contribution

It presents a novel algorithm that combines representation theory with combinatorial methods to improve invariant ring computation for permutation groups.

Findings

Reduces linear algebra computations in invariant theory

Uses a combinatorial description to simplify calculations

Provides an efficient algorithm for permutation group invariants

Abstract

Using the theory of representations of the symmetric group, we propose an algorithm to compute the invariant ring of a permutation group. Our approach have the goal to reduce the amount of linear algebra computations and exploit a thinner combinatorial description of the invariant ring.