7 papers · 1 filter
Algebraic Invariants of Edge Ideals Under Suspension
Selvi Kara, Dalena Vien
The central question of this paper is: how do algebraic invariants of edge ideals change under natural graph operations? We study this question through the lens of suspensions. The…
Neural codes via homological invariants of polarized neural ideals
Selvi Kara, Ellie Lew
For a neural code , polarizing the canonical form generators of the neural ideal yields a squarefree monomial ideal $\mathcal{…
Realizable (reg, deg h)-Pairs for Cover Ideals via Independence Polynomials
Jennifer Biermann, Trung Chau, Selvi Kara +4
Let be a finite simple graph on vertices and set , with edge ideal and cover ideal . We give an explicit description of the -polynom…
Computation of dominant ideals
Anna Maria Bigatti, Nursel Erey, Selvi Kara +4
We consider the problem of determining whether a monomial ideal is dominant. This property is critical for determining for which monomial ideals the Taylor resolution is minimal. W…
Minimal Cellular Resolutions of Path Ideals
Trung Chau, Selvi Kara, Kyle Wang
In this paper, we prove that the path ideals of both paths and cycles have minimal cellular resolutions. Specifically, these minimal free resolutions coincide with the Barile-Macch…
Gapfree graphs and powers of edge ideals with linear quotients
Nursel Erey, Sara Faridi, TÃ i Huy HÃ +3
Let be the edge ideal of a gapfree graph . An open conjecture of Nevo and Peeva states that has linear resolution for . We present a promising approach t…