A. A. Pour

activity

20122025

most citedMonomial ideals with 3-linear resolutions

15 citations · 26 across the 10 of their papers we have counts for

collaborators

14 papers

math.CO2025

Positive matching decompositions of the cartesian product of graphs

Mohammad Farrokhi Derakhshandeh Ghouchan, Ali Akbar Yazdan Pour

Let $Γ = (V, E)$ be a finite simple graph. A matching $M \subseteq E$ is positive if there exists a weight function on $V$ such that the matching $M$ is characterized by those edges w…

math.AC2023

Gröbner basis and Krull dimension of Lovász-Saks-Sherijver ideal associated to a tree

Mohammad Farrokhi Derakhshandeh Ghouchan, Ali Akbar Yazdan Pour

Let $K$ be a field and $n$ be a positive integer. Let $Γ = ([n], E)$ be a simple graph, where $[n] = {1, \dots, n}$ . If $S = K [x_{1}, \dots, x_{n}, y_{1}, \dots, y_{n}]$ is…

math.AC2022

Cellular resolutions of monomial ideals and their Artinian reductions

Sara Faridi, Mohammad Farrokhi Derakhshandeh Ghouchan, Roghayyeh Ghorbani +1

The question we address in this paper is: which monomial ideals have minimal cellular resolutions, that is, minimal resolutions obtained from homogenizing the chain maps of CW-comp…

math.AC2021

Shedding vertices and Ass-decomposable monomial ideals

Raheleh Jafari, Ali Akbar Yazdan Pour

The shedding vertices of simplicial complexes are studied from an algebraic point of view. Based on this perspective, we introduce the class of ass-decomposable monomial ideals whi…

math.AC2021

Extending simplicial complexes: Topological and combinatorial properties

Mohammad Farrokhi Derakhshandeh Ghouchan, Alireza Shamsian, Ali Akbar Yazdan Pour

Given an arbitrary hypergraph $H$ , we may glue to $H$ a family of hypergraphs to get a new hypergraph $H^{'}$ having $H$ as an induced subhyper…

math.CO2021

Positive matching decompositions of graphs

Mohammad Farrokhi Derakhshandeh Ghouchan, Shekoofeh Gharakhloo, Ali Akbar Yazdan Pour

A matching $M$ in a graph $Γ$ is positive if $Γ$ has a vertex-labeling such that $M$ coincides with the set of edges with positive weights. A positive matching decomposition (pmd)…

math.AC2020

Multigraded minimal free resolutions of simplicial subclutters

Mina Bigdeli, Ali Akbar Yazdan Pour

This paper concerns the study of a class of clutters called simplicial subclutters. Given a clutter $C$ and its simplicial subclutter $D$ , we compare some algeb…

math.AC2020

The Valabrega-Valla modules of monomial ideals

Abbas Nasrollah Nejad, Ali Akbar Yazdan Pour

In this paper, we focus on the initial degree and the vanishing of the Valabrega-Valla module of a pair of monomials ideals $J \subseteq I$ in a polynomials ring over a field $\math…

math.AC2016

Tame graphs, clutters and their Rees algebras

Abbas Nasrollah Nejad, Ashkan Nikseresht, Ali Akbar Yazdan Pour +1

A tame ideal is an ideal $I$ such that the blowup of the affine space $A_{k}^{n}$ along $I$ is regular. In this paper, we give a combinatorial characterization of tame squaref…

math.AC2015

Stability of Betti numbers under reduction processes: towards chordality of clutters

Mina Bigdeli, Ali Akbar Yazdan Pour, Rashid Zaare-Nahandi

For a given clutter $C$ , let $I := I (C ˉ)$ be the circuit ideal in the polynomial ring $S$ . In this paper, we show that the Betti numbers of $I$ and $I + (…

math.AC2015

Candidates for non-zero Betti numbers of monomial ideals

Ali Akbar Yazdan Pour

Let $I$ be a monomial ideal in the polynomial ring $S$ generated by elements of degree at most $d$ . In this paper, it is shown that, if the $i$ -th syzygy of $I$ has no element of d…

math.AC2012★ 11 cited

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…

math.AC2012

Regularity and Free Resolution of Ideals which are Minimal to $d$ -linearity