The depth function of powers of cover ideals of path graphs

TL;DR

This paper derives explicit formulas for the depth functions of powers of cover ideals in path graphs, enhancing understanding of their algebraic properties.

Contribution

It provides the first explicit formulas for the depth functions of powers of cover ideals specifically for path graphs.

Findings

Explicit formulas for depth functions of powers of cover ideals of paths

Application of Hochster's depth formula to path graphs

Improved understanding of algebraic invariants of path graph ideals

Abstract

Let $G=P_n$ be a path graph with cover ideal $J(P_n)$. By using Hochster's depth formula, we prove the explicit formulae to compute the depth functions of powers of cover ideals of paths.