Celebrating Loday’s associahedron
Vincent Pilaud, Francisco Santos, Günter M. Ziegler
Abstract
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 where 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.
Topics & Concepts
MathematicsCluster algebraDiagonalVertex (graph theory)CombinatoricsLattice (music)Congruence relationAlgebra over a fieldPure mathematicsGeometryGraphQuantumQuantum mechanicsAcousticsPhysicsAdvanced Combinatorial MathematicsAlgebraic structures and combinatorial modelsAdvanced Topics in Algebra