Guangjun Zhu

collaborators

8 papers

math.AC2026

Depth of powers of the edge ideal of an increasing weighted path

Jiaxin Li, Dancheng Lu, Thanh Vu +1

We provide exact formulas for the depth of the quotient ring of powers of the edge ideal of an increasing weighted path.

math.AC2026

The regularity of monomial ideals and their integral closures

Yijun Cui, Cheng Gong, Guangjun Zhu

Let $I$ be a monomial ideal in a polynomial ring $S = K [x_{1}, \dots, x_{n}]$ over a field $K$ with $n = 2$ or $3$ , and let $I$ be its integral closure. We will show that $\text{…

math.AC2025

Depth of powers of integrally closed edge ideals of edge-weighted paths

Jiaxin Li, Thanh Vu, Guangjun Zhu

We compute the depth of powers of edge ideals of integrally closed edge-weighted paths.

math.AC2025

Depth and regularity of powers of edge ideals of edge-weighted trees

Truong Thi Hien, Jiaxin Li, Tran Nam Trung +1

For an increasing weighted tree $G_{I ¨} $ , we obtain an asymptotic value and a sharp bound on the index stability of the depth function of its edge ideal $I (G_{I ¨} )$ . Moreover, if $G_Ï…

math.AC2025

Cohen-Macaulayness of Powers of Edge Ideals of Weighted Oriented Graphs

Truong Thi Hien, Jiaxin Li, Tran Nam Trung +1

For the edge ideal $I(\D)$ of a weighted oriented graph $\D$, we prove that its symbolic powers $I(\D)^{(t)}$ are Cohen-Macaulay for all $t ⩾ 1$ if and only if the underlyin…

math.AC2025

Associated primes of powers of edge ideals of edge-weighted trees

Jiaxin Li, Tran Nam Trung, Guangjun Zhu

In this paper, we give a complete description of the associated primes of each power of the edge ideal of an increasing weighted tree.