Separating trees and simple congruences of the weak order
Abstract
A congruence of the weak order is simple if its quotientope is a simple polytope. We provide an alternative elementary proof of the characterization of the simple congruences in terms of forbidden up and down arcs. For this, we provide a combinatorial description of the vertices of the corresponding quotientopes in terms of separating trees. This also yields a combinatorial description of all faces of the corresponding quotientopes. We finally explore algebraic aspects of separating trees, in particular their connections with quiver representation theory.
Fields of Study & Subjects
Advanced Algebra and Logic
Publication details
- Journal / source
- European Journal of Combinatorics
- Volume
- 136
- Pages
- 104375–104375
- Publication date
- 27 March 2026
- Language
- EN