# Depth of powers of squarefree monomial ideals

## TL;DR

This paper establishes new bounds for the depth of powers of squarefree monomial ideals linked to hyperforests, extending previous bounds based on hypergraph domination and regular sequences.

## Contribution

It introduces two general bounds for the depths of powers of squarefree monomial ideals associated with hyperforests, broadening existing theoretical frameworks.

## Key findings

- Derived bounds generalize previous results
- Bounds relate to hypergraph domination numbers
- Applicable to powers of squarefree monomial ideals

## Abstract

We derive two general bounds for the depths of powers of squarefree monomial ideals corresponding to hyperforests. These bounds generalize known bounds for the depths of squarefree monomial ideals, which were given in terms of the edgewise domination number of the corresponding hypergraphs and the lengths of initially regular sequences with respect to the ideals.