Shiya Duan

activity

20222024

collaborators

Showing math.ACShow all

5 papers · 1 filter

math.AC2024

Powers of edge ideals of edge-weighted trees

Jiaxin Li, Guangjun Zhu, Shiya Duan

This paper gives exact formulas for the regularity of edge ideals of edge-weighted integrally closed trees. In addition, we provide some linear upper bounds on the regularity of po…

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.AC2022

Freiman Borel type ideals

Guangjun Zhu, Yakun Zhao, Shiya Duan +1

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