# Packing properties of cubic squarefree monomial ideals

## TL;DR

This paper investigates when symbolic and ordinary powers of cubic squarefree monomial ideals are equal, providing a classification for cubic path ideals with this property.

## Contribution

It offers a complete classification of cubic path ideals where symbolic and ordinary powers coincide, advancing understanding of their algebraic properties.

## Key findings

- Classified all cubic path ideals with coinciding symbolic and ordinary powers.
- Identified conditions under which these powers are equal for cubic squarefree monomial ideals.
- Enhanced understanding of the algebraic structure of cubic path ideals.

## Abstract

The symbolic powers, in general, are not equal to the ordinary powers. Therefore, one interesting question here is for what classes of ideals ordinary and symbolic powers coincide? The answer to this question for squarefree monomial ideals may be packing property. In this paper, we classify all cubic path ideals for those the symbolic and ordinary powers coincide.