Forcing the weak Lefschetz property for equigenerated monomial ideals

TL;DR

This paper classifies the minimal number of generators needed for certain monomial ideals to ensure the associated algebra has the weak Lefschetz property, advancing understanding of algebraic structures with this property.

Contribution

It provides a classification of minimal generator counts for artinian equigenerated monomial ideals that guarantee the weak Lefschetz property.

Findings

Identifies minimal generator thresholds for the weak Lefschetz property

Classifies ideals based on their generator counts

Advances understanding of algebraic structures with Lefschetz properties

Abstract

We classify the minimal number of generators of artinian equigenerated monomial ideals $I$ such that $\Bbbk[x_1,\ldots,x_n]/I$ is forced to have the weak Lefschetz property.