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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…
Polymatroidal ideals and their asymptotic syzygies
Antonino Ficarra, Dancheng Lu
Let be a polymatroidal ideal. In this paper, we study the asymptotic behavior of the homological shift ideals of powers of polymatroidal ideals. We prove that the first homolog…
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…