Zexin Wang

activity

20222026

collaborators

11 papers

math.AC2026

Homology of non-matching complexes under edge additions and applications to their Stanley-Reisner ideals

Jiawen Shan, Zexin Wang

For a bipartite graph $G$ and an integer $t \geq 2$ , let $\NM_t(G)$ be its $t$ -non-matching complex. We prove that adding an edge while preserving bipartiteness induces an injection…

math.AC2025

Homological shifts of powers a complementary edge ideal

Dancheng Lu, Zexin Wang, Guangjun Zhu

The homological shift algebra and the projective dimension function of complementary edge ideals are investigated. Let $G$ be a connected graph, and let $I$ be its complementary ed…

math.AC2025

Betti Numbers of Edge Ideals of Weighted Oriented Crown Graphs

Zexin Wang, Dancheng Lu

We compute the multigraded Betti numbers of edge ideals for weighted oriented crown graphs using a novel approach. This approach, which we still call the \emph{induced subgraph app…

math.AC2025

Betti numbers of normal edge rings (II)

Zexin Wang, Dancheng Lu

We compute the Betti numbers of the edge rings of multi-path graphs using the \emph{induced-subgraph approach} introduced in \cite{WL1}. Here, a multi-path graph refers to a simple…

math.AC2024

The Multiplicity of Powers of a Class of Non-Square-free Monomial Ideals

Liuqing Yang, Zexin Wang

Let $R = K [x_{1}, \dots, x_{n}]$ be a polynomial ring over a field $K$ , and let $I \subseteq R$ be a monomial ideal of height $h$ . We provide a formula for the multi…

math.AC2024

Betti numbers of normal edge rings (\bf{I})

Zexin Wang, Dancheng Lu

We introduce a novel approach named the {\it induced-subgraph approach} for investigating the Betti numbers of normal edge rings. Utilizing this approach, we compute all the multig…

math.AC2024

Multiplicity of powers of path ideals of a line graph

Jiawen Shan, Zexin Wang, Dancheng Lu

Let $S = K [x_{1}, \dots, x_{n}]$ and let $I$ be the $t$ -path ideal of the line graph $L_{n}$ with $n$ -vertices. It is shown that the set of associated prime ideals of $I^{s}$ is equal to the…

math.AC2023

The resolutions of generalized co-letterplace ideals and their powers

Dancheng Lu, Zexin Wang

We present a natural and explicit multigraded minimal free resolution for each generalized co-letterplace ideal (see Definition 1.1). Our resolution differs significantly from the…

math.AC2023

The edge rings of compact graphs

Zexin Wang, Dancheng Lu

We define a simple graph as compact if it lacks even cycles and satisfies the odd-cycle condition. Our focus is on classifying all compact graphs and examining the characteristics…

math.AC2023

Correction to: Powers of the vertex cover ideals (Collect. Math. 65 (2014) 169--181)

Dancheng Lu, Zexin Wang

We point out an essential gap in the proof of one of main results in \cite{M} and then give a corrected proof for it.

math.AC2022

On powers of the cover ideals of graphs

Dancheng Lu, Zexin Wang

For a simple graph $G$ , assume that $J (G)$ is the vertex cover ideal of $G$ and $J (G)^{(s)}$ is the $s$ -th symbolic power of $J (G)$ . We prove that $(J (C)^{(s)}) = (J (C)^{s})$ for all $…