Augustine O’Keefe

activity

20112021

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4 papers · 1 filter

math.AC2021

Toric Ideals of Weighted Oriented Graphs

Jennifer Biermann, Selvi Kara, Kuei-Nuan Lin +1

Given a vertex-weighted oriented graph, we can associate to it a set of monomials. We consider the toric ideal whose defining map is given by these monomials. We find a generating…

math.AC2019

Betti numbers of symmetric shifted ideals

Jennifer Biermann, Hernán De Alba, Federico Galetto +5

We introduce a new class of monomial ideals which we call symmetric shifted ideals. Symmetric shifted ideals are fixed by the natural action of the symmetric group and, within the…

math.AC2016

Bounds on the regularity of toric ideals of graphs

Jennifer Biermann, Augustine O'Keefe, Adam Van Tuyl

Let $G$ be a finite simple graph. We give a lower bound for the Castelnuovo-Mumford regularity of the toric ideal $I_{G}$ associated to $G$ in terms of the sizes and number of induce…

math.AC2011

Depth of initial ideals of normal edge rings

Takayuki Hibi, Akihiro Higashitani, Kyouko Kimura +1

Let $G$ be a finite graph on the vertex set $[d] = {1, ..., d}$ with the edges $e_{1}, ..., e_{n}$ and $K[\tb] = K[t_1, ..., t_d]$ the polynomial ring in $d$ variables over a field…