On the strong persistence property and normally torsion-freeness of square-free monomial ideals

TL;DR

This paper investigates the strong persistence property of square-free monomial ideals, provides a criterion related to the Conforti-Cornuejols conjecture, and characterizes normally torsion-freeness of their linear combinations.

Contribution

It establishes the strong persistence property for ideals in five variables, offers a criterion for minimal counterexamples to a conjecture, and characterizes normally torsion-free sums.

Findings

Square-free monomial ideals in five variables have the strong persistence property.

A criterion for identifying minimal counterexamples to the Conforti-Cornuejols conjecture.

A necessary and sufficient condition for the normal torsion-freeness of sums of such ideals.

Abstract

In this paper, we first show that any square-free monomial ideal in $K[x_1, x_2, x_3, x_4, x_5]$ has the strong persistence property. Next we will provide a criterion for a minimal counterexample to the Conforti-Cornuejols conjecture. Finally we give a necessary and sufficient condition to determine the normally torsion-freeness of a linear combination of two normally torsion-free square-free monomial ideals.