Yijun Cui

activity

20212025

collaborators

11 papers

math.AC2025

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 edge ideals of edge-weighted integrally closed cycles

Guangjun Zhu, Jiaxin Li, Yijun Cui +1

This paper gives some exact formulas for the depth of powers of the edge ideal of an edge-weighted integrally closed cycle.

math.AC2024

Regularity of powers of edge ideals of edge-weighted integrally closed cycles

Guangjun Zhu, Yijun Cui, Jiaxin Li +1

This paper gives exact formulas for the regularity of powers of edge ideals of an edge-weighted integrally closed cycle.

math.AC2024

Edge ideals of some edge-weighted graphs

Guangjun Zhu, Shiya Duan, Yijun Cui +1

This paper presents exact formulas for the regularity and depth of powers of edge ideals of an edge-weighted star graph. Additionally, we provide exact formulas for the regularity…

math.AC2023

The $\circ$ operation and $*$ operation of Cohen-Macaulay bipartite graphs

Yulong Yang, Guangjun Zhu, Yijun Cui +1

Let $G$ be a finite simple graph with the vertex set $V$ and let $I_{G}$ be its edge ideal in the polynomial ring $S = K [x_{V}]$ . In this paper, we compute the depth and the Cas…

math.AC2023

Integral closure and normality of edge ideals of some edge-weighted graphs

Shiya Duan, Guangjun Zhu, Yijun Cui +1

Let $G_{ω}$ be an edge-weighted simple graph. In this paper, we give a complete characterization of the graph $G_{ω}$ whose edge ideal $I (G_{ω})$ is integrally closed. We also show that…

math.AC2023

The $\circ$ operation and $*$ operation of fan graphs

Guangjun Zhu, Yijun Cui, Yulong Yang +1

Let $G$ be a finite simple graph on the vertex set $V$ and let $I_{G}$ denote its edge ideal in the polynomial ring $S = K [x_{V}]$ . In this paper, we compute the depth and the C…

math.AC2022

The edge ideals of the join of some vertex weighted oriented graphs

Yijun Cui, Guangjun Zhu, Xiaoqi Wei

In this paper, we describe primary decomposition of the edge ideal of the join of some graphs in terms of that information of the edge ideal of every weighted oriented graph. Meanw…

math.AC2021

The facet ideals of matching complexes of line graphs

Guangjun Zhu, Hong Wang, Yijun Cui

Let $L_{n}$ be a line graph with $n$ edges and $\F(L_n)$ the facet ideal of its matching complex. In this paper, we provide the irreducible decomposition of $\F(L_n)$ and some exact…

math.AC2021

Freiman $t$ -spread principal Borel ideals

Guangjun Zhu, Yakun Zhao, Yijun Cui

An equigenerated monomial ideal $I$ is a Freiman ideal if $μ (I^{2}) = ℓ (I) μ (I) - (2 ℓ ( I ))$ where $ℓ (I)$ is the analytic spread of $I$ and $μ (I)$ is the least number of mo…

math.AC2021

Freiman cover ideals of unmixed bipartite graphs

Guangjun Zhu, Yakun Zhao, Yijun Cui

An equigenerated monomial ideal $I$ in the polynomial ring $R = k [z_{1}, \dots, z_{n}]$ is a Freiman ideal if $μ (I^{2}) = ℓ (I) μ (I) - (2 ℓ ( I ))$ where $ℓ (I)$ is the analytic spre…

The regularity of monomial ideals and their integral closures

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

Regularity of powers of edge ideals of edge-weighted integrally closed cycles

Edge ideals of some edge-weighted graphs

The ∘ operation and ∗ operation of Cohen-Macaulay bipartite graphs

Integral closure and normality of edge ideals of some edge-weighted graphs

The ∘ operation and ∗ operation of fan graphs

The edge ideals of the join of some vertex weighted oriented graphs

The facet ideals of matching complexes of line graphs

Freiman t-spread principal Borel ideals

Freiman cover ideals of unmixed bipartite graphs

The $\circ$ operation and $*$ operation of Cohen-Macaulay bipartite graphs

The $\circ$ operation and $*$ operation of fan graphs

Freiman $t$ -spread principal Borel ideals