Mohammed Rafiq Namiq

activity

20222026

most citedThe graded Betti numbers of truncation of ideals in polynomial rings

1 citations · 1 across the 10 of their papers we have counts for

collaborators

11 papers

math.CO2026

Hilbert functions of filtered graphical zonotopal algebras

Boris Shapiro, Ilya Smirnov, Arkady Vaintrob

The external zonotopal algebra of a graph is generated by nilpotent vertex elements $X_{v}$ and determines the graphical matroid after deleting loops. Replacing these generators by $…

math.AC2026

Regularity of Symbolic Powers of Co-Chordal Edge Ideals

Chwas Ahmed, Mohammed Rafiq Namiq

Let $G$ be a finite simple co-chordal graph with at least one edge, and let $I (G)$ be its edge ideal. Over an arbitrary field, we prove that the symbolic powers of $I (G)$ satisfy $…

math.CO2026

A Complete Classification of 2-Linear Neighborhood Complexes

Mohammed Rafiq Namiq

Let $G$ be a nonempty finite simple graph. We study when the Stanley-Reisner ideal of its neighborhood complex has a $2$ -linear resolution. Combining Fröberg's theorem with the cla…

math.AC2026

Betti Numbers of Sequentially Cohen-Macaulay Co-Chordal Graphs and Their Applications

Mohammed Rafiq Namiq

We study edge ideals of sequentially Cohen-Macaulay co-chordal graphs through the maximal-clique structure of their chordal complements. After making the required construction orde…

math.AC2026

Explicit Betti Numbers for Skeletons of Chordal Clique Complexes and Their Alexander Duals

Mohammed Rafiq Namiq

Let $Δ_{r} = Δ_{r} (n_{1}, \dots, n_{e})$ be the clique complex of a chordal graph with maximal cliques $S_{1}, \dots, S_{e}$ in a leaf order, where $n_{m} = ∣ S_{m} ∣$ , $r_m=|S_{m+1}\c…

math.AC2026

Vertex Dismissibility and Scalability of Simplicial Complexe

Mohammed Rafiq Namiq

We study three nonpure extensions of vertex decomposability, shellability, and Cohen-Macaulayness at the minimum facet dimension. For $b = indim Δ$ , strong vertex dismi…

math.AC2025

Initially Cohen-Macaulay Modules

Mohammed Rafiq Namiq

In this paper, we introduce initially Cohen-Macaulay modules over a commutative Noetherian local ring $R$ , a new class of $R$ -modules that generalizes both Cohen-Macaulay and seque…

math.AC2025

The Graded Betti Numbers of the Skeletons of Simplicial Complexes

Mohammed Rafiq Namiq

In this paper, we study a class $C$ of squarefree monomial ideals $I \subseteq R = K [x_{1}, \dots, x_{n}]$ over a field $K$ , defined by the condition that $\dim…

math.AC2022★ 1 cited

The graded Betti numbers of truncation of ideals in polynomial rings

Chwas Ahmed, Ralf Fröberg, Mohammed Rafiq Namiq

Let $R = K [x_{1}, \dots, x_{n}]$ , a graded algebra $S = R / I$ satisfies $N_{k, p}$ if $I$ is generated in degree $k$ , and the graded minimal resolution is linear the first $p$ steps,…

math.AC2022

Quasi-forest simplicial complexes and almost Cohen-Macaulay

Chwas Ahmed, Amir Mafi, Mohammed Rafiq Namiq

In this paper we study the quasi-forest simplicial complexes and we define the concept of simplicial $k$ -cycle (denoted by $S_{k}$ ) and simplicial $k$ -point (denoted by $\m…

math.AC2022

Sequentially Cohen-Macaulay Co-Chordal Graphs: Structure and Projective Dimension

Chwas Ahmed, Amir Mafi, Mohammed Rafiq Namiq

We introduce a class of chordal graphs called ( $d_{1}$ , $d_{2}$ , $\dots$ , $d_{q}$ )-trees. A graph belongs to this class if and only if its clique complex is sequentially Cohen-Macaulay, pro…