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.

中文翻译：

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庆祝洛迪的联合面体

我们调查了让·路易斯·洛迪 (Jean-Louis Loday) 对关联面体的顶点描述，及其对组合学、离散几何和代数的深远影响。我们特别提出了它发挥核心作用的四个主题：弱阶的格同余及其商、簇代数及其广义关联面体、嵌套复形及其嵌套面体、以及操作数和关联面体对角线。