Stability of depth functions of cover ideals of balanced hypergraphs

TL;DR

This paper proves that the depth functions of cover ideals of balanced hypergraphs are non-increasing and provides bounds for their depth stability index, advancing understanding of algebraic properties of these combinatorial structures.

Contribution

It establishes the non-increasing property of depth functions and offers bounds for the depth stability index of cover ideals of balanced hypergraphs.

Findings

Depth functions are non-increasing.

Bounds are provided for the depth stability index.

Results enhance understanding of algebraic invariants of hypergraph ideals.

Abstract

We prove that the depth functions of cover ideals of balanced hyper- gragh have the non-increasing property. Furthermore, we also give a bound for the index of depth stability of these ideals.