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Vertex barycenter of generalized associahedra. (English) Zbl 1316.52022
The paper makes use of the following construction: the convex hull of the orbit of a point in the Euclidean space under the action of some Weyl group is a generalized permutahedron. The removal of some of its defining inequalities leaves a generalized associahedron. It is proven that the vertex barycenter of generalized associahedra and permutahedra coincide.

MSC:
52B15 Symmetry properties of polytopes
13F60 Cluster algebras
52B05 Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.)
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