9 citations · 10 across the 5 of their papers we have counts for
6 papers
Extended Weak Order for the Rank 3 Universal Coxeter Group
Grant Barkley, Colin Defant, Patricia Hersh +3
The weak order is a classical poset structure on a Coxeter group; it is a lattice when the group is finite but merely a meet-semilattice when the group is infinite. Motivated by pr…
The Affine Tamari Lattice
Grant Barkley, Colin Defant
Given a fixed integer , we construct two new finite lattices that we call the cyclic Tamari lattice and the affine Tamari lattice. The cyclic Tamari lattice is a sublattic…
FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI
Elliot Glazer, Ege Erdil, Tamay Besiroglu +21
We introduce FrontierMath, a benchmark of hundreds of original, exceptionally challenging mathematics problems crafted and vetted by expert mathematicians. The questions cover most…
On two notions of total positivity for generalized partial flag varieties of classical Lie types
Grant Barkley, Jonathan Boretsky, Christopher Eur +1
For Grassmannians, Lusztig's notion of total positivity coincides with positivity of the Plucker coordinates. This coincidence underpins the rich interaction between matroid theory…
Oriented matroid structures on rank 3 root systems
Grant Barkley, Katherine Tung
We show that, given a rank 3 affine root system with Weyl group , there is a unique oriented matroid structure on which is -equivariant and restricts to the usual mat…
Bender--Knuth Billiards in Coxeter Groups
Grant Barkley, Colin Defant, Eliot Hodges +2
Let be a Coxeter system, and write , where is a finite index set. Fix a nonempty convex subset of . If is of type , then $\mat…