S. Fakhari

activity

20122024

most citedRegularity of Powers of edge ideal of very well-covered graphs

8 citations · 17 across the 20 of their papers we have counts for

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24 papers · 1 filter

math.AC2024

Induced matching, ordered matching and Castelnuovo-Mumford regularity of bipartite graphs

A. V. Jayanthan, S. A. Seyed Fakhari, I. Swanson +1

Let G be a finite simple graph and let indm(G) and ordm(G) denote the induced matching number and the ordered matching number of G, respectively. We characterize all bipartite grap…

math.AC2023

An Increasing normalized depth function

S. A. Seyed Fakhari

Let $K$ be a field and $S = K [x_{1}, \dots, x_{n}]$ be the polynomial ring in $n$ variables over $K$ . Assume that $I$ is a squarefree monomial ideal of $S$ . For…

math.AC2023

On the Castelnuovo-Mumford regularity of symbolic powers of cover ideals

S. A. Seyed Fakhari

Assume that $G$ is a graph with cover ideal $J (G)$ . For every integer $k \geq 1$ , we denote the $k$ -th symbolic power of $J (G)$ by $J (G)^{(k)}$ . We provide a sharp upper bound for t…

math.AC2022

Lower bounds for the depth of second power of edge ideals

S. A. Seyed Fakhari

Assume that $G$ is a graph with edge ideal $I (G)$ . We provide sharp lower bounds for the depth of $I (G)^{2}$ in terms of the star packing number of $G$ .

math.AC2020

On the minimal free resolution of symbolic powers of cover ideals of graphs

S. A. Seyed Fakhari

For any graph $G$ , assume that $J (G)$ is the cover ideal of $G$ . Let $J (G)^{(k)}$ denote the $k$ th symbolic power of $J (G)$ . We characterize all graphs $G$ with the property that $…

math.AC2020★ 3 cited

On the depth of symbolic powers of edge ideals of graphs

S. A. Seyed Fakhari

Assume that $G$ is a graph with edge ideal $I (G)$ and star packing number $α_{2} (G)$ . We denote the $s$ -th symbolic power of $I (G)$ by $I (G)^{(s)}$ . It is shown that the inequality $…

math.AC2019

On the regularity of small symbolic powers of edge ideals of graphs

S. A. Seyed Fakhari

Assume that $G$ is a graph with edge ideal $I (G)$ and let $I (G)^{(s)}$ denote the $s$ -th symbolic power of $I (G)$ . It is proved that for every integer $s \geq 1$ , $${\rm reg}(I(G)^{…

math.AC2019★ 3 cited

Regularity of symbolic powers of edge ideals of Cameron-Walker graphs

S. A. Seyed Fakhari

A Cameron-Walker graph is a graph for which the matching number and the induced matching number are the same. Assume that $G$ is a Cameron-Walker graph with edge ideal $I (G)$ , and…

math.AC2019

On the Stanley depth of powers of monomial ideals

S. A. Seyed Fakhari

Let $K$ be a field and $S = K [x_{1}, \dots, x_{n}]$ be the polynomial ring in $n$ variables over $K$ . In 1982, R. Stanley associated a combinatorial invariant to…

math.AC2019★ 1 cited

Regularity of symbolic powers of edge ideals of unicyclic graphs

S. A. Seyed Fakhari

Let $G$ be a unicyclic graph with edge ideal $I (G)$ . For any integer $s \geq 1$ , we denote the $s$ -th symbolic power of $I (G)$ by $I (G)^{(s)}$ . It is shown that ${\rm reg}(I(G)^{(s)…

math.AC2018

On the depth and Stanley depth of integral closure of powers of monomial ideals

S. A. Seyed Fakhari

Let $K$ be a field and $S = K [x_{1}, \dots, x_{n}]$ be the polynomial ring in $n$ variables over $K$ . Assume that $G$ is a graph with edge ideal $I (G)$ . We prove…

math.AC2018

Improved bounds for the regularity of powers of edge ideals of graphs

Seyed Amin Seyed Fakhari, Siamak Yassemi

Let $G$ be a graph with edge ideal $I (G)$ . We recall the notions of $min - ma t c h_{{K_{2}, C_{5}}} (G)$ and $\ind-match_{\{K_2, C_5\}}(G)$ from \cite{sy}. We show that $${\rm reg}(I(G)^…

math.AC2017

Depth and Stanley depth of symbolic powers of cover ideals of graphs

S. A. Seyed Fakhari

Let $G$ be a graph with $n$ vertices and let $S = K [x_{1}, \dots, x_{n}]$ be the polynomial ring in $n$ variables over a field $K$ . Assume that $J (G)$ is the cover ideal…

math.AC2017

Regularity of symbolic powers of cover ideals of graphs

S. A. Seyed Fakhari

Let $G$ be a graph which belongs to either of the following classes: (i) bipartite graphs, (ii) unmixed graphs, or (iii) claw--free graphs. Assume that $J (G)$ is the cover ideal $G…

math.AC2017★ 8 cited

Regularity of Powers of edge ideal of very well-covered graphs

Pooran Norouzi, Seyed Amin Seyed Fakhari, Siamak Yassemi

Let $k \geq 3$ be an integer and $G$ be a very well-covered graph with $odd - girth (G) \geq 2 k + 1$ . Assume that $I (G)$ is the edge ideal of $G$ . We show that for every integer $s$ …

math.AC2017★ 1 cited

On the regularity of edge ideal of graphs

Seyed Amin Seyed Fakhari, Siamak Yassemi

Let $G$ be a graph with $n$ vertices, $S = K [x_{1}, \dots, x_{n}]$ be the polynomial ring in $n$ variables over a field $K$ and $I (G)$ denote the edge ideal of $G$ . For e…

math.AC2017

On the $h$ -vector of ( $S_{r}$ ) simplicial complexes

S. A. Seyed Fakhari

We give a negative answer to a question proposed in [3], regarding the $h$ -vector of ( $S_{r}$ ) simplicial complexes.

math.AC2016

Depth, Stanley depth and regularity of ideals associated to graphs

S. A. Seyed Fakhari

Let $K$ be a field and $S = K [x_{1}, \dots, x_{n}]$ be the polynomial ring in $n$ variables over $K$ . Let $G$ be a graph with $n$ vertices. Assume that $I = I (G)$ …

math.AC2016

Symbolic powers of cover ideal of very well-covered and bipartite graphs

S. A. Seyed Fakhari

Let $G$ be a graph with $n$ vertices and $S = K [x_{1}, \dots, x_{n}]$ be the polynomial ring in $n$ variables over a field $K$ . Assume that $J (G)$ is the cover ideal of $…

math.AC2015

Regularity of powers of edge ideal of whiskered cycles

Mahdieh Moghimian, Seyed Amin Seyed Fakhari, Siamak Yassemi

Let $G = W (C_{n})$ be a whiskered cycle graph with edge ideal $I = I (G)$ . We prove that for every $s \geq 1$ , the equality $reg (I^{s}) = 2 s + ⌈ \frac{n - 1}{2} ⌉ - 1$ holds.

math.AC2015

On the Stanley depth and size of monomial ideals

S. A. Seyed Fakhari

Let $K$ be a field and $S = K [x_{1}, ..., x_{n}]$ be the polynomial ring in $n$ variables over the field $K$ . For every monomial ideal $I \subset S$ , We provide a…

math.AC2014

Two lower bounds for the Stanley depth of monomial ideals

Lukas Katthän, Seyed Amin Seyed Fakhari

Let $J  I$ be two monomial ideals of the polynomial ring $S = K [x_{1}, \dots, x_{n}]$ . In this paper, we provide two lower bounds for the Stanley depth of $I / J$ . On t…

math.AC2013

Stanley depth of weakly polymatroidal ideals and squarefree monomial ideals

S. A. Seyed Fakhari

Let $I$ be a weakly polymatroidal ideal or a squarefree monomial ideal of a polynomial ring $S$ . In this paper we provide a lower bound for the Stanley depth of $I$ and $S / I$ . In p…

math.AC2012

The Golod property for products and high symbolic powers of monomial ideals

S. A. Seyed Fakhari, Volkmar Welker

We show that for any two proper monomial ideals I and J in the polynomial ring S = k[x_1, ..., x_n] the ring S/IJ is Golod. We also show that if I is squarefree then for large enou…

Induced matching, ordered matching and Castelnuovo-Mumford regularity of bipartite graphs

An Increasing normalized depth function

On the Castelnuovo-Mumford regularity of symbolic powers of cover ideals

Lower bounds for the depth of second power of edge ideals

On the minimal free resolution of symbolic powers of cover ideals of graphs

On the depth of symbolic powers of edge ideals of graphs

On the regularity of small symbolic powers of edge ideals of graphs

Regularity of symbolic powers of edge ideals of Cameron-Walker graphs

On the Stanley depth of powers of monomial ideals

Regularity of symbolic powers of edge ideals of unicyclic graphs

On the depth and Stanley depth of integral closure of powers of monomial ideals

Improved bounds for the regularity of powers of edge ideals of graphs

Depth and Stanley depth of symbolic powers of cover ideals of graphs

Regularity of symbolic powers of cover ideals of graphs

Regularity of Powers of edge ideal of very well-covered graphs

On the regularity of edge ideal of graphs

On the h-vector of (Sr​) simplicial complexes

Depth, Stanley depth and regularity of ideals associated to graphs

Symbolic powers of cover ideal of very well-covered and bipartite graphs

Regularity of powers of edge ideal of whiskered cycles

On the Stanley depth and size of monomial ideals

Two lower bounds for the Stanley depth of monomial ideals

Stanley depth of weakly polymatroidal ideals and squarefree monomial ideals

The Golod property for products and high symbolic powers of monomial ideals

On the $h$ -vector of ( $S_{r}$ ) simplicial complexes