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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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…