Graham Keiper

activity

20182020

collaborators

4 papers

math.AC2020

Density of $f$ -ideals and $f$ -ideals in mixed small degrees

Huy TÀi HÀ, Graham Keiper, Hasan Mahmood +1

A squarefree monomial ideal is called an $f$ -ideal if its Stanley-Reisner and facet simplicial complexes have the same $f$ -vector. We show that $f$ -ideals generated in a fixed degr…

math.AC2020

Regularity and h-polynomials of toric ideals of graphs

Giuseppe Favacchio, Graham Keiper, Adam Van Tuyl

For all integers $4 \leq r \leq d$ , we show that there exists a finite simple graph $G = G_{r, d}$ with toric ideal $I_{G} \subset R$ such that $R / I_{G}$ has (Castelnuovo-Mumford) regula…

math.AC2019

Splittings of Toric Ideals

Giuseppe Favacchio, Johannes Hofscheier, Graham Keiper +1

Let $I \subseteq R = K [x_{1}, \dots, x_{n}]$ be a toric ideal, i.e., a binomial prime ideal. We investigate when the ideal $I$ can be "split" into the sum of two smaller toric…

math.AC2018

Betti numbers of toric ideals of graphs: A case study

Federico Galetto, Johannes Hofscheier, Graham Keiper +3

We compute the graded Betti numbers for the toric ideal of a family of graphs constructed by adjoining a cycle to a complete bipartite graph. The key observation is that this famil…

Density of f-ideals and f-ideals in mixed small degrees

Regularity and h-polynomials of toric ideals of graphs

Splittings of Toric Ideals

Betti numbers of toric ideals of graphs: A case study

Density of $f$ -ideals and $f$ -ideals in mixed small degrees