Circulant matrices and Galois-Togliatti systems

TL;DR

This paper compares the coefficients of the permanent and determinant of a circulant matrix and applies this comparison to prove a conjecture about the minimality of Galois-Togliatti systems.

Contribution

It introduces a novel comparison between permanent and determinant coefficients for circulant matrices and proves a conjecture on Galois-Togliatti systems' minimality.

Findings

Coefficients in permanent and determinant expansions are compared.

A conjecture on the minimality of Galois-Togliatti systems is proven.

The study enhances understanding of circulant matrices and algebraic systems.

Abstract

The goal of this article is to compare the coefficients in the expansion of the permanent with those in the expansion of the determinant of a three-lines circulant matrix. As an application we prove a conjecture concerning the minimality of Galois-Togliatti systems.