Abed Abedelfatah

activity

20102026

most citedOn the Eisenbud-Green-Harris Conjecture

4 citations · 4 across the 5 of their papers we have counts for

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9 papers · 1 filter

math.AC2026

Maximal shifts below the Taylor bound

Abed Abedelfatah

Let $I \subseteq S$ be a monomial ideal with minimal generator degrees between $e$ and $d$ , where $2 \leq e \leq d$ . We prove that if $t_{a} (S / I) < e a$ , then $$ t_{a+b}(S/I)\leq t_a(S/I)+…

math.AC2026

Two Infinite Families of Regular Sequences of Power Sums in Three Variables

Abed Abedelfatah

Let $S = C [x, y, z], p_{m} = x^{m} + y^{m} + z^{m} .$ For every $r \geq 1$ , we prove that $p_{r}, p_{r + 1}, p_{3 r + 1} and p_{r}, p_{r + 1}, p_{3 r + 2}$ are regular s…

math.AC2026

Quadratic Ideals in Six Variables and the Eisenbud--Green--Harris Conjecture

Abed Abedelfatah

In this paper, we study the Eisenbud--Green--Harris (EGH) conjecture for ideals generated by quadrics. We establish a sharp lower bound for the dimension of the cubic component of…

math.AC2023

On the subadditivity condition of edge ideal

Abed Abedelfatah

Let $S = K [x_{1}, \dots, x_{n}]$ , where $K$ is a field, and $t_{i} (S / I)$ denotes the maximal shift in the minimal graded free $S$ -resolution of the graded algebra $S / I$ at degree $i$ , where…

math.AC2020

Some results on the subadditivity condition of syzygies

Abed Abedelfatah

Among other results, we prove that if $I$ is a monomial ideal of $S = K [x_{1}, \dots, x_{n}]$ , where $K$ is a field, and $a \geq b - 1 \geq 0$ are integers such that $a+b\leq\mathrm{proj~dim}(…

math.AC2015

On vanishing patterns in $j$ -strands of edge ideals

Abed Abedelfatah, Eran Nevo

We consider two problems regarding vanishing patterns in the Betti table of edge ideals $I$ in polynomial algebra $S$ . First, we show that the $j$ -strand is connected if $j = 3$ (for…

Maximal shifts below the Taylor bound

Two Infinite Families of Regular Sequences of Power Sums in Three Variables

Quadratic Ideals in Six Variables and the Eisenbud--Green--Harris Conjecture

On the subadditivity condition of edge ideal

Some results on the subadditivity condition of syzygies

On vanishing patterns in j-strands of edge ideals

On vanishing patterns in $j$ -strands of edge ideals