S. Fakhari

activity

20182026

most citedStability of depth and Stanley depth of symbolic powers of squarefree monomial ideals

2 citations · 4 across the 14 of their papers we have counts for

collaborators

14 papers

math.AC2026

Bounded powers of edge ideals: Nearly Gorenstein polytopes

Takayuki Hibi, Seyed Amin Seyed Fakhari

A lattice polytope $P \subset R^{n}$ of dimension $n$ is called nearly Gorenstein if $P$ is normal and if its Ehrhart ring is a nearly Gorenstein ring. W…

math.AC2026

Componentwise linear monomial ideals

Takayuki Hibi, Seyed Amin Seyed Fakhari

Let $S = K [x_{1}, \dots, x_{n}]$ denote the polynomial ring in $n$ variables over a field $K$ with $deg x_{1} = \dots = deg x_{n} = 1$ and ${\bf a} = (a_1,\ldots,a_n) \in {\mathbb Z…

math.AC2026

Regularity and depth of binomial ideals arising from combinatorics

Takayuki Hibi, Seyed Amin Seyed Fakhari

Regularity and depth of binomial ideals generated by adjacent $2$ -minors together with those arising from finite lattices are studied.

math.AC2026

An algebraic study of ideals of weak graph homomorphisms

Francesco Navarra, Ayesha Asloob Qureshi, Seyed Amin Seyed Fakhari

Let $G$ and $H$ be finite simple graphs and assume that either both are undirected or both are directed. We introduce and study the ideal of weak graph homomorphisms $I_{G \to H}$ .…

math.AC2026

Depth of edge ideals and vertex connectivity of finite graphs

Takayuki Hibi, Seyed Amin Seyed Fakhari

Let $G$ be a finite graph on $[n] := {1, \dots, n}$ and $κ (G)$ its vertex connectivity. Let $S = K [x_{1}, \dots, x_{n}]$ denote the polynomial ring in $n$ variables over a field $K$ an…

math.AC2026

Partially ordered sets of distributive type and algebras with straightening laws

Takayuki Hibi, Seyed Amin Seyed Fakhari

A finite poset (partially ordered set) $P$ with $0^$ is called of distributive type if every interval $[0^, a]$ , $a \in P$ , of $P$ is a distributive lattice. From a vie…

math.AC2025

Bounded powers of edge ideals: Pseudo-Gorenstein and Level polytopes

Takayuki Hibi, Seyed Amin Seyed Fakhari

A lattice polytope $P \subset R^{n}$ of dimension $n$ is called level* if (i) $P$ is normal, (ii) $(\mathcal{P} \setminus \partial \mathcal{P}) \cap \mat…

math.AC2025

Bounded powers of edge ideals: Gorenstein polytopes

Takayuki Hibi, Seyed Amin Seyed Fakhari

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

math.AC2025

Bounded powers of edge ideals: symmetric exchange binomials

Takayuki Hibi, Seyed Amin Seyed Fakhari

It has been conjectured that the toric ideal of the base ring of a discrete polymatroid is generated by symmetric exchange binomials. In the present paper, we give several classes…

math.AC2025

Bounded powers of edge ideals: The strong exchange property

Takayuki Hibi, Seyed Amin Seyed Fakhari

Let $S = K [x_{1}, \dots, x_{n}]$ denote the polynomial ring in $n$ variables over a field $K$ and $I \subset S$ a monomial ideal. Given a vector $c \in Z_{> 0}^{n}$ , the i…

math.AC2025

Bounded powers of edge ideals: Gorenstein toric rings

Takayuki Hibi, Seyed Amin Seyed Fakhari

Let $S = K [x_{1}, \dots, x_{n}]$ denote the polynomial ring in $n$ variables over a field $K$ and $I \subset S$ a monomial ideal. Given a vector $c \in N^{n}$ , the ideal…

math.AC2025

Bounded powers of edge ideals: regularity and linear quotients

Takayuki Hibi, Seyed Amin Seyed Fakhari

Let $S = K [x_{1}, \dots, x_{n}]$ denote the polynomial ring in $n$ variables over a field $K$ and let $I \subset S$ be a monomial ideal. For a vector $c \in N^{n}$ , we se…

math.AC2023

On the Regularity of squarefree part of symbolic powers of edge ideals

S. A. Seyed Fakhari

Assume that $G$ is a graph with edge ideal $I (G)$ . For every integer $s \geq 1$ , we denote the squarefree part of the $s$ -th symbolic power of $I (G)$ by $I (G)^{{s}}$ . We determine…

math.AC2018★ 2 cited

Stability of depth and Stanley depth of symbolic powers of squarefree 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 $I \subset S$ is a squarefree monomial ideal. Fo…