Quotientopes

Abstract

For any lattice congruence of the weak order on ${\mathfrak{S}}_n$, N. Reading proved that glueing together the cones of the braid fan that belong to the same congruence class defines a complete fan. We prove that this fan is the normal fan of a polytope.

14 pages, 9 figures; Version 3: Minor changes

References in corpus (8)

• Cambrian Lattices
• Lattice congruences, fans and Hopf algebras
• The brick polytope of a sorting network
• Algebraic and combinatorial structures on pairs of twin binary trees
• The Hopf algebra of diagonal rectangulations
• Cambrian Hopf Algebras
• Associahedra via spines
• Brick polytopes, lattice quotients, and Hopf algebras

Cited by in corpus (10)

• Celebrating Loday's Associahedron
• Shard polytopes
• Shuffles of deformed permutahedra, multiplihedra, constrainahedra, and biassociahedra
• Rectangulotopes
• Hochschild polytopes
• The $s$-weak order and $s$-permutahedra I: combinatorics and lattice structure
• Geometric realizations of the $s$-weak order and its lattice quotients
• Deformed graphical zonotopes
• Separating trees and simple congruences of the weak order
• Pebble trees