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math.AC2026
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…
math.AC2026
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…
math.AC2026
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…