6 papers
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…
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…
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…