7 papers · 1 filter
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 yiel…
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…
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…
The Pop-Stack Operator on Ornamentation Lattices
Khalid Ajran, Colin Defant
Each rooted plane tree has an associated ornamentation lattice . The ornamentation lattice of an -element chain is the -th Tamari lattic…