A. Nikseresht

activity

20162024

most citedChordality of Clutters with Vertex Decomposable Dual and Ascent of Clutters

14 citations · 42 across the 14 of their papers we have counts for

collaborators

15 papers

cs.IT2024

Linear Complementary Equi-Dual Codes

Ashkan Nikseresht, Shohreh Namazi, Marziyeh Beygi Khormaei

We call a linear code $C$ with length $n$ over a field $F$ , a linear complementary equi-dual code, when there exists a linear code $D$ over $F$ such that $D$ is permutation equival…

math.CO2024

Well-covered Unit Graphs of Finite Rings

Shahin Rahimi, Ashkan Nikseresht

Let $R$ be a finite ring with identity. The unit graph (unitary Cayley graph) of $R$ is the graph with vertex set $R$ , where two distinct vertices $x$ and $y$ are adjacent exactly…

math.CO2023★ 1 cited

Well-covered Unitary Cayley Graphs of Matrix Rings over Finite Fields and Applications

Shahin Rahimi, Ashkan Nikseresht

Suppose that $F$ is a finite field and $R = M_{n} (F)$ is the ring of $n$ -square matrices over $F$ . Here we characterize when the Cayley graph of the additive group of $R$ with respect…

cs.IT2022

One-Sided Repeated-Root Two-Dimensional Cyclic and Constacyclic Codes

Marziyeh Beygi Khormaei, Ashkan Nikseresht, Shohreh Namazi

In this paper, we study some repeated-root two-dimensional cyclic and constacyclic codes over a finite field $F = F_{q}$ . We obtain the generator matrices and generator polyno…

math.AC2021★ 3 cited

Gorenstein and Cohen-Macaulay Matching Complexes

Ashkan Nikseresht

Let $H$ be a simple undirected graph. The family of all matchings of $H$ forms a simplicial complex called the matching complex of $H$ . Here , we give a classification of all graph…

math.AC2020★ 1 cited

Algebraic Properties of Clique Complexes of Line Graphs

Ashkan Nikseresht

Let $H$ be a simple undirected graph and $G = L (H)$ be its line graph. Assume that $Δ (G)$ denotes the clique complex of $G$ . We show that $Δ (G)$ is sequentially Cohen-Macaul…

math.CO2019★ 3 cited

Some Combinatorial Characterizations of Gorenstein Graphs with Independence Number Less than Four

Mohammad Reza Oboudi, Ashkan Nikseresht

Let $α = α (G)$ be the independence number of a simple graph $G$ with $n$ vertices and $I (G)$ be its edge ideal in $S = K [x_{1}, \dots, x_{n}]$ . If $S / I (G)$ is Gorenstein, the graph $G$ is…

math.AC2019★ 1 cited

On Gorenstein Circulant Graphs and Gorenstein SQC Graphs

Ashkan Nikseresht, Mohammad Reza Oboudi

We characterize some graphs with a Gorenstein edge ideal. In particular, we show that if $G$ is a circulant graph with vertex degree at most four or a circulant graph of the form $…

math.AC2019★ 6 cited

Trung's Construction and the Charney-Davis Conjecture

Ashkan Nikseresht, Mohammad Reza Oboudi

We consider a construction by which we obtain a simple graph $T (H, v)$ from a simple graph $H$ and a non-isolated vertex $v$ of $H$ . We call this construction "Trung's cons…

math.AC2017★ 14 cited

Chordality of Clutters with Vertex Decomposable Dual and Ascent of Clutters

Ashkan Nikseresht

In this paper, we consider the generalization of chordal graphs to clutters proposed by Bigdeli, et al in J. Combin. Theory, Series A (2017). Assume that $C$ is a $d$ -dim…

math.AC2017

Factorizations in Modules and Splitting Multiplicatively Closed Subsets

Ashkan Nikseresht

We introduce the concept of multiplicatively closed subsets of a commutative ring $R$ which split an $R$ -module $M$ and study factorization properties of elements of $M$ with respe…

cs.IT2016★ 3 cited

Dual of Codes over Finite Quotients of Polynomial Rings

Ashkan Nikseresht

Let $A = \frac{F [ x ]}{⟨ f ( x )⟩}$ , where $f (x)$ is a monic polynomial over a finite field $F$ . In this paper, we study the relation between $A$ -codes and…

math.AC2016

Finite Commutative Rings with a MacWilliams Type Relation for the m-Spotty Hamming Weight Enumerators

Ashkan Nikseresht

Let $R$ be a finite commutative ring. We prove that a MacWilliams type relation between the m-spotty weight enumerators of a linear code over $R$ and its dual hold, if and only if,…

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.CO2016★ 10 cited

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…