8 papers
Noncrossing Combinatorics, the Full Twist, and Decategorification of Knot Invariants
Colin Defant, Nathan Williams
Much work in knot theory has consisted of categorifying, and thereby strengthening, knot invariants. We take the opposite approach: decategorification, more commonly called combina…
Permutahedron Triangulations via Total Linear Stability and the Dual Braid Group
Colin Defant, Melissa Sherman-Bennett, Nathan Williams
For each finite Coxeter group and each standard Coxeter element of , we construct a triangulation of the -permutahedron. For particular realizations of the -permutahed…
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…
Rowmotion and Echelonmotion
Colin Defant, Yuhan Jiang, Rene Marczinzik +4
Given a linear extension of a finite poset , we consider the permutation matrix indexing the Schubert cell containing the Cartan matrix of with respect to . This yi…
Chute Move Posets are Lattices
Ilani Axelrod-Freed, Colin Defant, Hanna Mularczyk +2
For each permutation , we consider the set of reduced pipe dreams for , partially ordered so that cover relations correspond to (generalized) chute moves. Se…
Reduced Random Walks in the Hyperbolic Plane
Colin Defant, Mitchell Lee
We study Lam's reduced random walk in a hyperbolic triangle group, which we view as a random walk in the upper half-plane. We prove that this walk converges almost surely to a poin…