6 papers
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…
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…
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…
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 m…