22 citations · 65 across the 17 of their papers we have counts for
24 papers
On the Betti numbers of monomial ideals and their powers
Reza Abdolmaleki, Rashid Zaare-Nahandi
Let the polynomial ring over a field . In this paper for some families of monomial ideals we study the minimal number of ge…
Toric ideals which are determinantal
Reza Abdolmaleki, Rashid Zaare-Nahandi
Given any equigenerated monomial ideal with the property that the defining ideal of the fiber cone of is generated by quadratic binomials, we introduce a matrix…
On the initial behaviour of the number of generators of powers of monomial ideals
Reza Abdolmaleki, Jürgen Herzog, Rashid Zaare-Nahandi
Given a number , we construct a monomial ideal with the property that the function which describes the number of generators of has at least local maxima.
Decomposable clutters and a generalization of Simon's conjectutre
Mina Bigdeli, Ali Akbar Yazdan Pour, Rashid Zaare-Nahandi
Each (equigenerated) squarefree monomial ideal in the polynomial ring represents a family of subsets of , called a (uniform) clutter. In this…
Torsion-free Aluffi Algebras
Abbas Nasrollah Nejad, Zahra Shahidi, Rashid Zaare-Nahandi
A pair of ideals has been called Aluffi torsion-free if the Aluffi algebra of is isomorphic with the corresponding Rees algebra. We give necessary a…
Unmixed d-uniform r-partite hypergraphs
Reza Jafarpour-Golzari, Rashid Zaare-Nahandi
In this paper, we characterize all unmixed d-uniform r-partite hypergraphs under a certain condition. Also we give a necessary condition for unmixedness in d-uniform hypergraphs wi…
Tame graphs, clutters and their Rees algebras
Abbas Nasrollah Nejad, Ashkan Nikseresht, Ali Akbar Yazdan Pour +1
A tame ideal is an ideal such that the blowup of the affine space along is regular. In this paper, we give a combinatorial characterization of tame squaref…
Simplicial orders and chordality
Mina Bigdeli, Jürgen Herzog, Ali Akbar Yazdan Pour +1
Chordal clutters in the sense of [14] and [3] are defined via simplicial orders. Their circuit ideal has a linear resolution, independent of the characteristic of the base field. W…
On Generalizations of Cycles and Chordality to Hypergraphs from an Algebraic Viewpoint
Ashkan Nikseresht, Rashid Zaare-Nahandi
In this paper, we study the notion of chordality and cycles in hypergraphs from a commutative algebraic point of view. The corresponding concept of chordality in commutative algebr…
Unmixed r-partite graphs
Reza Jafarpoure Golzari, Rashid Zaare-Nahandi
Unmixed bipartite graphs have been characterized by Ravadra and Villarreal independently. Our aim in this paper is to characterize unmixed r-partite graphs under a certain conditio…
Stability of Betti numbers under reduction processes: towards chordality of clutters
Mina Bigdeli, Ali Akbar Yazdan Pour, Rashid Zaare-Nahandi
For a given clutter , let be the circuit ideal in the polynomial ring . In this paper, we show that the Betti numbers of and $I + (…
The Aluffi algebra of the Jacobian of points in projective space: torsion-freeness
Abbas Nasrollah Nejad, Aron Simis, Rashid Zaare-Nahandi
The algebra in the title has been introduced by P. Aluffi. Let be ideals in the commutative ring . The (embedded) Aluffi algebra of on is an intermediate…
On the index of powers of edge ideals
Mina Bigdeli, Juergen Herzog, Rashid Zaare-Nahandi
The index of a graded ideal measures the number of linear steps in the graded minimal free resolution of the ideal. In this paper we study the index of powers and squarefree powers…
Cohen-Macaulay -partite graphs with minimal clique cover
Asghar Madadi, Rashid Zaare-Nahandi
In this note, we give some necessary conditions for an -partite graph such that the edge ring of the graph is Cohen-Macaulay. It is proved that if is an -partite Cohen-Ma…
Regularity of edge ideal of a graph
Marcel Morales, Ali Akbar Yazdan Pour, Rashid Zaare-Nahandi
In this paper, we introduce some reduction processes on graphs which preserve the regularity of related edge ideals. As a consequence, an alternative proof for the theorem of R. Fr…
Regularity and Free Resolution of Ideals which are Minimal to -linearity
Marcel Morales, Ali Akbar Yazdan Pour, Rashid Zaare-Nahandi
Toward a partial classification of monomial ideals with -linear resolution, in this paper, some classes of -uniform clutters which do not have linear resolution, but every pr…
Monomial ideals with 3-linear resolutions
Marcel Morales, Abbas Nasrollah Nejad, Ali Akbar Yazdan Pour +1
In this paper, we study Cstelnuovo-Mumford regularity of square-free monomial ideals generated in degree 3. We define some operations on the clutters associated to such ideals and…
Universally Koszul algebras defined by graphs
Rashid Zaare-Nahandi
In this note, it is proved that a graphs is -free if and only if its edge ring is universally Koszul. Using properties of this family of graphs, we show that Universall…
Pure simplicial complexes and well-covered graphs
Rashid Zaare-Nahandi
A graph is called well-covered if all maximal independent sets of vertices have the same cardinality. A simplicial complex is called pure if all of its facets have the same…
Aluffi torsion-free ideals
Abbas Nasrollah Nejad, Rashid Zaare-Nahandi
A special class of algebras which are intermediate between the symmetric and the Rees algebras of an ideal was introduced by P. Aluffi in 2004 to define characteristic cycle of a h…
Cohen-Macaulayness of bipartite graphs, revisited
Rashid Zaare-Nahandi
Cohen-Macaulayness of bipartite graphs is investigated by several mathematicians and has been characterized combinatorially. In this note, we give some different combinatorial cond…
Invariance of the Barycentric Subdivision of a Simplicial Complex
Rashid Zaare-Nahandi
In this paper we show that a simplicial complex can be determined uniquely up to isomorphism by its barycentric subdivision or comparability graph. At the end, it is summarized sev…
Well-covered and uniformly well-covered graphs
Rashid Zaare-Nahandi
A graph is called well-covered if all maximal independent sets of vertices have the same cardinality. A well-covered graph is called uniformly well-covered if there is a pa…
On isomorphism of simplicial complexes and their related algebras
Rashid Zaare-Nahandi
In this paper, we provide a simple proof for the fact that two simplicial complexes are isomorphic if and only if their associated Stanley-Reisner rings, or their associated facet…