8 papers
A quasisymmetric analog of Grassmannian Schubert varieties
Teddy Gonzales, Tuong Le, Chayim Lowen
We show that the cohomology rings of toric Richardson varieties in the Grassmannian are finite truncations of the ring of quasisymmetric functions. We exhibit an affine paving of e…
On Smooth Combinatorial Products of Simplices
Juliana Curtis, Tuong Le, Chayim Lowen
We show that every lattice weak Minkowski summand of a smooth polytope combinatorially isomorphic to a product of simplices has a quadratic triangulation. This is achieved by ident…
Koszul Orlik--Solomon Algebras from Non-supersolvable Arrangements
Tuong Le, Chayim Lowen, Jason McCullough
The cohomology ring of the complement of a complex hyperplane arrangement is given by its Orlik--Solomon algebra. It is known that the defining ideal of the Orlik--Solomon algebra…
Matroid flat counts can have many peaks
Alexander Divoux, Matt Larson, Chayim Lowen +1
We disprove Rota's conjecture that the counts of flats in a matroid according to rank form a unimodal sequence. Furthermore, we show that this sequence can have arbitrarily many pe…
Matroid flat counts are not unimodal
Alexander Divoux, Chayim Lowen, Shouda Wang
We give counterexamples to Rota's 1970 conjecture that the sequence counting flats of varying rank in a matroid is unimodal. More specifically, inspired by Larson's recent disproof…
Structural properties of Białynicki-Birula decompositions
Teddy Gonzales, Chayim Lowen
We investigate several aspects of the Bialynicki-Birula decomposition of a smooth complete -variety with finite fixed locus. Our results include novel characterizatio…
On the asymptotic behavior of finite hyperfields
Tuong Le, Chayim Lowen
Hobby has recently shown that almost all finite hyperfields of even order fail to be the quotient of a field. Using a probabilistic argument, we extend this result to all orders: a…
Simultaneous generating sets for flags
Federico Glaudo, Noah Kravitz, Chayim Lowen
We prove that any triple of complete flags in admits a common generating set of size and that this bound is sharp. This result extends the class…