6 papers
Graded Betti numbers of graded Möbius algebras of uniform matroids
Louiza Fouli, Sean Grate, Selvi Kara +5
Graded Möbius algebras were a key tool in the proof of the Dowling-Wilson Top Heavy Conjecture. They are commutative algebras whose Hilbert functions recover the Whitney numbers of…
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…
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…
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…
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 augmen…
Ideals with Larger Projective Dimension and Regularity
Jesse Beder, Jason McCullough, Luis Nunez-Betancourt +3
We define a family of homogeneous ideals with large projective dimension and regularity relative to the number of generators and their common degree. This family subsumes and impro…