22 citations · 65 across the 17 of their papers we have counts for
21 papers · 1 filter
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…
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…
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…