2 citations · 7 across the 29 of their papers we have counts for
29 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…
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…
The operation and operation of Cohen-Macaulay bipartite graphs
Yulong Yang, Guangjun Zhu, Yijun Cui +1
Let be a finite simple graph with the vertex set and let be its edge ideal in the polynomial ring . In this paper, we compute the depth and the Cas…
Projective dimension and regularity of edge ideals of some vertex-weighted oriented unicyclic graphs
Guangjun Zhu, Hong Wang
In this paper we provide some exact formulas for the projective dimension and the regularity of edge ideals of vertex-weighted oriented unicyclic graphs. These formulas are in func…
Integral closure and normality of edge ideals of some edge-weighted graphs
Shiya Duan, Guangjun Zhu, Yijun Cui +1
Let be an edge-weighted simple graph. In this paper, we give a complete characterization of the graph whose edge ideal is integrally closed. We also show that…
Generalized binomial edge ideals of bipartite graphs
Yi-Huang Shen, Guangjun Zhu
Connected bipartite graphs whose binomial edge ideals are Cohen--Macaulay have been classified by Bolognini et al. In this paper, we compute the depth, Castelnuovo--Mumford regular…
The facet ideals of chessboard complexes
Chengyao Jiang, Yakun Zhao, Hong Wang +1
In this paper we describe the irreducible decomposition of the facet ideal $\F(Δ_{m,n})$ of the chessboard complex with . We also provide some lower bounds for d…
The edge ideals of the join of some vertex weighted oriented graphs
Yijun Cui, Guangjun Zhu, Xiaoqi Wei
In this paper, we describe primary decomposition of the edge ideal of the join of some graphs in terms of that information of the edge ideal of every weighted oriented graph. Meanw…
Freiman Borel type ideals
Guangjun Zhu, Yakun Zhao, Shiya Duan +1
An equigenerated monomial ideal in the polynomial ring is a Freiman ideal if where is the analytic spre…
Some homological properties of Borel type ideals
Jürgen Herzog, Somayeh Moradi, Masoomeh Rahimbeigi +1
We study ideals of Borel type, including -Borel ideals and -spread Veronese ideals. We determine their free resolutions and their homological shift ideals. The multiplicity a…
Regularity of powers of (parity) binomial edge ideals
Yi-Huang Shen, Guangjun Zhu
In this paper, we provide exact formulas for the Castelnuovo-Mumford regularity of powers of an almost complete intersection ideal which is generated by a homogeneous -seque…
The facet ideals of matching complexes of line graphs
Guangjun Zhu, Hong Wang, Yijun Cui
Let be a line graph with edges and $\F(L_n)$ the facet ideal of its matching complex. In this paper, we provide the irreducible decomposition of $\F(L_n)$ and some exact…
Freiman -spread principal Borel ideals
Guangjun Zhu, Yakun Zhao, Yijun Cui
An equigenerated monomial ideal is a Freiman ideal if where is the analytic spread of and is the least number of mo…
Freiman cover ideals of unmixed bipartite graphs
Guangjun Zhu, Yakun Zhao, Yijun Cui
An equigenerated monomial ideal in the polynomial ring is a Freiman ideal if where is the analytic spre…
Homological shift ideals
Jürgen Herzog, Somayeh Moradi, Masoomeh Rahimbeigi +1
For a monomial ideal , we consider the th homological shift ideal of , denoted by , that is, the ideal generated by the th multigraded shifts of . So…
The saturation number of $\cb$-bounded stable monomial ideals and their powers
Reza Abdolmaleki, Jürgen Herzog, Guangjun Zhu
Let be the polynomial ring in variables over a field . In this paper, we compute the socle of $\cb$-bounded strongly stable ideals and determine that t…
Sortable Freiman ideals
Jürgen Herzog, Guangjun Zhu
In this paper it is shown that a sortable ideal is Freiman if and only if its sorted graph is chordal. This characterization is used to give a complete classification of Freima…
Regularity and projective dimension of powers of edge ideal of the disjoint union of some weighted oriented gap-free bipartite graphs
Guangjun Zhu, Li Xu, Hong Wang +1
In this paper we provide some precise formulas for regularity of powers of edge ideal of the disjoint union of some weighted oriented gap-free bipartite graphs. For the projective…
On the fiber cone of monomial ideals
Jürgen Herzog, Guangjun Zhu
We consider the fiber cone of monomial ideals. It is shown that for monomial ideals of height , generated by elements, the fiber cone of is a hy…
Projective dimension and regularity of edge ideals of some vertex-weighted oriented -partite graphs
Guangjun Zhu, Hong Wang, Li Xu +1
In this paper we provide some exact formulas for the projective dimension and the regularity of edge ideals associated to three special types of vertex-weighted oriented -partit…
Projective dimension and regularity of powers of edge ideals of vertex-weighted rooted forests
Li Xu, Guangjun Zhu, Hong Wang +1
In this paper we provide some exact formulas for projective dimension and the regularity of powers of edge ideals of vertex-weighted rooted forests. These formulas are functions of…
Regularity of powers of edge ideals of vertex-weighted oriented unicyclic graphs
Guangjun Zhu, Hong Wang, Li Xu +1
In this paper we provide some exact formulas for the regularity of powers of edge ideals of vertex-weighted oriented cycles and vertex-weighted unicyclic graphs. These formulas are…
Projective dimension and regularity of edge ideal of some weighted oriented graphs
Guangjun Zhu, Li Xu, Hong Wang +1
In this paper we provide some exact formulas for the projective dimension and the regularity of edge ideals associated to vertex weighted rooted forests and oriented cycles. As som…
The relevance of Freiman's theorem for combinatorial commutative algebra
Jürgen Herzog, Takayuki Hibi, Guangjun Zhu
Freiman's theorem gives a lower bound for the cardinality of the doubling of a finite set in $\RR^n$. In this paper we give an interpretation of his theorem for monomial ideals and…