4 papers
Standard Monomials for Positroid Varieties
Ayah Almousa, Shiliang Gao, Daoji Huang
We give an explicit characterization of the standard monomials for positroid varieties with respect to the Hodge degeneration and give a Gröbner basis. Furthermore, we show that p…
Ribbon complexes for the 0-Hecke algebra
Ayah Almousa, Bryan Lu
We construct explicit tableau-level maps between indecomposable projective modules for the type A 0-Hecke algebra that assemble into canonical split short exact sequences lifting t…
Koszulity, supersolvability, and Stirling representations
Ayah Almousa, Victor Reiner, Sheila Sundaram
Supersolvable hyperplane arrangements and matroids are known to give rise to certain Koszul algebras, namely their Orlik-Solomon algebras and graded Varchenko-Gel'fand algebras. We…
Root polytopes, tropical types, and toric edge ideals
Ayah Almousa, Anton Dochtermann, Ben Smith
We consider arrangements of tropical hyperplanes where the apices of the hyperplanes are taken to infinity in certain directions. Such an arrangement defines a decomposition of Euc…