19 citations · 22 across the 8 of their papers we have counts for
10 papers
The MorseResolutions package for Macaulay2
Trung Chau, Selvi Kara, Augustine O'Keefe
Using discrete Morse theory, Batzies and Welker introduced Morse resolutions of monomial ideals. In this note, we present the {\it Macaulay2} package {\tt MorseResolutions} for wor…
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…
Algebraic invariants of weighted oriented graphs
Selvi Kara, Jennifer Biermann, Kuei-Nuan Lin +1
Let be a weighted oriented graph and let be its edge ideal in a polynomial ring . We give the formula of Castelnuovo-Mumford regularity of $R/I(\m…
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…
Algebraic properties of toric rings of graphs
Selvi Kara, Huy Tai Ha, Augustine O'Keefe
Let be a simple graph. We investigate the Cohen-Macaulayness and algebraic invariants, such as the Castelnuovo-Mumford regularity and the projective dimension, of the t…
Bounds on the regularity of toric ideals of graphs
Jennifer Biermann, Augustine O'Keefe, Adam Van Tuyl
Let be a finite simple graph. We give a lower bound for the Castelnuovo-Mumford regularity of the toric ideal associated to in terms of the sizes and number of induce…