Celebrating Loday's Associahedron

Abstract

We survey Jean-Louis Loday's vertex description of the associahedron, and its far reaching influence in combinatorics, discrete geometry and algebra. We present in particular four topics were it plays a central role: lattice congruences of the weak order and their quotientopes, cluster algebras and their generalized associahedra, nested complexes and their nestohedra, and operads and the associahedron diagonal.

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Cited by in corpus (7)

• Shuffles of deformed permutahedra, multiplihedra, constrainahedra, and biassociahedra
• Realizations of multiassociahedra via rigidity
• 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
• Separating trees and simple congruences of the weak order