4 papers
Properties of LCM Lattices of Monomial Ideals
Matthew Dorang, Jason McCullough
LCM lattices were introduced by Gasharov, Peeva, and Welker as a way to study minimal free resolutions of monomial ideals. All LCM lattices are atomic and all atomic lattices arise…
F-Purity of Binomial Edge Ideals
Adam LaClair, Jason McCullough
In 2012, K. Matsuda introduced the class of weakly closed graphs and investigated when binomial edge ideals are F-pure. He proved that weakly closed binomial edge ideals are F-pure…
Koszul Binomial Edge Ideals
Adam LaClair, Matthew Mastroeni, Jason McCullough +1
As the binomial edge ideal of a graph is always generated by homogeneous quadratic polynomials corresponding to the edges of the graph, the question of when a binomial edge ideal d…
Koszul Graded Möbius Algebras and Strongly Chordal Graphs
Adam LaClair, Matthew Mastroeni, Jason McCullough +1
The graded Möbius algebra of a matroid is a commutative graded algebra which encodes the combinatorics of the lattice of flats of the matroid. As a special subalgebra of the augme…