1 citations · 1 across the 9 of their papers we have counts for
9 papers
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…
The chain algebra of a pure poset
Dancheng Lu
We extend the notion of chain algebra, originally defined in \cite{GN} for finite distributive lattices, to that of finite pure posets. We show this algebra corresponds to the Ehrh…
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…
Multiplicity of powers of path ideals of a line graph
Jiawen Shan, Zexin Wang, Dancheng Lu
Let and let be the -path ideal of the line graph with -vertices. It is shown that the set of associated prime ideals of is equal to the…
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…
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…