10 papers · 1 filter
Homology of non-matching complexes under edge additions and applications to their Stanley-Reisner ideals
Jiawen Shan, Zexin Wang
For a bipartite graph and an integer , let $\NM_t(G)$ be its -non-matching complex. We prove that adding an edge while preserving bipartiteness induces an injection…
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 be a connected graph, and let be its complementary ed…
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…
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…
The Multiplicity of Powers of a Class of Non-Square-free Monomial Ideals
Liuqing Yang, Zexin Wang
Let be a polynomial ring over a field , and let be a monomial ideal of height . We provide a formula for the multi…
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…