6 papers
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…
Powers of graphs & applications to resolutions of powers of monomial ideals
Susan M. Cooper, Sabine El Khoury, Sara Faridi +4
This paper is concerned with the question of whether geometric structures such as cell complexes can be used to simultaneously describe the minimal free resolutions of all powers o…
Simplicial resolutions for the second power of square-free monomial ideals
Susan M. Cooper, Sabine El Khoury, Sara Faridi +4
Given a square-free monomial ideal , we define a simplicial complex labeled by the generators of which supports a free resolution of . As a consequence, we obtain (sh…
Morse resolutions of powers of square-free monomial ideals of projective dimension one
Susan Cooper, Sabine El Khoury, Sara Faridi +4
Let be a square-free monomial ideal of projective dimension one. Starting with the Taylor complex on the generators of , we use Discrete Morse theory to describe a CW…
Asymptotic stabilization of Betti diagrams of generic initial systems
Sarah Mayes-Tang
Several authors investigating the asymptotic behaviour of the Betti diagrams of the graded system obtained by taking powers of an ideal have shown that the shape of the nonzero ent…
Stabilization of Boij-Söderberg Decompositions of Ideal Powers
Sarah Mayes-Tang
Given an ideal we investigate the decompositions of Betti diagrams of the graded family of ideals formed by taking powers of . We prove conjectures of Engström…