Susan M. Cooper

collaborators

4 papers

math.AC2021

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…

math.AC2021

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 $I$ , we define a simplicial complex labeled by the generators of $I^{2}$ which supports a free resolution of $I^{2}$ . As a consequence, we obtain (sh…

math.AC2021

Morse resolutions of powers of square-free monomial ideals of projective dimension one

Susan Cooper, Sabine El Khoury, Sara Faridi +4

Let $I$ be a square-free monomial ideal $I$ of projective dimension one. Starting with the Taylor complex on the generators of $I^{r}$ , we use Discrete Morse theory to describe a CW…

math.AC2018

Generalized minimum distance functions and algebraic invariants of Geramita ideals

Susan M. Cooper, Alexandra Seceleanu, Stefan O. Tohaneanu +2

Motivated by notions from coding theory, we study the generalized minimum distance (GMD) function $δ_{I} (d, r)$ of a graded ideal $I$ in a polynomial ring over an arbitrary field usin…