Sabine El Khoury

activity

20122026

collaborators

10 papers

math.AC2026

Cellular resolutions of second powers of square-free monomial ideals with divisibility relations

Susan M. Cooper, Sabine El Khoury, Sara Faridi +3

Using divisibility relations between the generators of a square-free monomial ideal $I$ , we describe divisibility relations between the generators of the second power $I^{2}$ . We the…

math.AC2024

Artinian Gorenstein algebras of embedding dimension four and socle degree three over an arbitrary field

Sabine El Khoury, Andrew R. Kustin

Let k be an arbitrary field, A be a standard graded Artinian Gorenstein k-algebra of embedding dimension four and socle degree three, and pi from P to A be a surjective graded homo…

math.AC2023

The Scarf complex and betti numbers of powers of extremal ideals

Sabine El Khoury, Sara Faridi, Liana Sega +1

This paper is concerned with finding bounds on betti numbers and describing combinatorially and topologically (minimal) free resolutions of powers of ideals generated by a fixed nu…

math.AC2022

Quadratically presented Gorenstein ideals

Sabine El Khoury, Andrew R. Kustin

Let $J$ be a quadratically presented grade three Gorenstein ideal in the standard graded polynomial ring $R = k [x, y, z]$ , where $k$ is a field. Assume that $R / J$ satisfies the weak L…

math.AC2022

Simplicial Resolutions of Powers of Square-free Monomial Ideals

Susan M. Cooper, Sabine El Khoury, Sara Faridi +4

The Taylor resolution is almost never minimal for powers of monomial ideals, even in the square-free case. In this paper we introduce a smaller resolution for each power of any squ…

math.AC2016

A note on the subadditivity of Syzygies

Sabine El Khoury, Hema Srinivasan

Let $R = S / I$ be a graded algebra with $t_{i}$ and $T_{i}$ being the minimal and maximal shifts in the minimal $S$ resolution of $R$ at degree $i$ . In this paper we prove that $t_n\leq t…

math.AC2014

The structure of Gorenstein-linear resolutions of Artinian algebras

Sabine El Khoury, Andrew R. Kustin

This is the third paper in a series of three papers. The first two papers in the series are called "Artinian Gorenstein algebras with linear resolutions", (arXiv:1306.2523) and "Th…

math.AC2014

The explicit minimal resolution constructed from a Macaulay inverse system

Sabine El Khoury, Andrew R. Kustin

This is the second paper in a series of three papers. In the first paper of the series, "Artinian Gorenstein algebras with linear resolutions", (arXiv:1306.2523, J. of Algebra, to…

math.AC2013

Artinian Gorenstein algebras with linear resolutions

Sabine El Khoury, Andrew R. Kustin

Fix a pair of positive integers d and n. We create a ring R and a complex G of R-modules with the following universal property. Let P be a polynomial ring in d variables over a fie…

math.AC2012

Gorenstein Hilbert Coefficients

Sabine El Khoury, Hema Srinivasan

We prove upper and lower bounds for all the coefficients in the Hilbert Polynomial of a graded Gorenstein algebra $S = R / I$ with a quasi-pure resolution over $R$ . The bounds are in t…