6 papers
The Non-Lefschetz Locus of Monomial Complete Intersections in Positive Characteristic
Adam LaClair
In the 1980s, Stanley and J. Watanabe proved that over a field of characteristic zero every monomial complete intersection has the strong Lefschetz property. Determining which mono…
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…
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…
The MatrixSchubert package for Macaulay2
Ayah Almousa, Sean Grate, Daoji Huang +4
We introduce the MatrixSchubert package for the computer algebra system Macaulay2. This package has tools to construct and study matrix Schubert varieties and alternating sign matr…