8 papers
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…
Duals of algebraic matroids need not be algebraic
Matt Larson, Tuong Le
We give an example showing that the dual of an algebraic matroid need not be algebraic. Our example is a matroid of rank 6 on 10 elements which is algebraic in characteristic 2. It…
Skew Hives, Skew Skeps, Skew Schur Log-Concavity
Tuong Le, Son Nguyen
Knutson and Tao's hives is a combinatorial model to compute Littlewood--Richardson coefficients. Similar to hives, Speyer introduced skeps and used them to prove a Schur log-concav…
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…
On symmetric pattern avoidance sets
Tuong Le
For a set of permutations , consider the quasisymmetric generating function where $\mathrm{Des}(w) := \{i\mid w(i)>…
Notes on the Linear Algebraic View of Regularity Lemmas
Greg Bodwin, Tuong Le
When regularity lemmas were first developed in the 1970s, they were described as results that promise a partition of any graph into a ``small'' number of parts, such that the graph…
Improved Online Reachability Preservers
Greg Bodwin, Tuong Le
A reachability preserver is a basic kind of graph sparsifier, which preserves the reachability relation of an -node directed input graph among a set of given demand pairs $P…
Quantum bumpless pipe dreams
Tuong Le, Shuge Ouyang, Leo Tao +2
Schubert polynomials are polynomial representatives of Schubert classes in the cohomology of the complete flag variety and have a combinatorial formulation in terms of bumpless pip…