4 citations · 4 across the 5 of their papers we have counts for
9 papers
Maximal shifts below the Taylor bound
Abed Abedelfatah
Let be a monomial ideal with minimal generator degrees between and , where . We prove that if , then $$ t_{a+b}(S/I)\leq t_a(S/I)+…
Two Infinite Families of Regular Sequences of Power Sums in Three Variables
Abed Abedelfatah
Let For every , we prove that are regular s…
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…
On the subadditivity condition of edge ideal
Abed Abedelfatah
Let , where is a field, and denotes the maximal shift in the minimal graded free -resolution of the graded algebra at degree , where…
Some results on the subadditivity condition of syzygies
Abed Abedelfatah
Among other results, we prove that if is a monomial ideal of , where is a field, and are integers such that $a+b\leq\mathrm{proj~dim}(…
On vanishing patterns in -strands of edge ideals
Abed Abedelfatah, Eran Nevo
We consider two problems regarding vanishing patterns in the Betti table of edge ideals in polynomial algebra . First, we show that the -strand is connected if (for…