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Coxeter complexes and graph-associahedra. (English) Zbl 1099.52001
The authors suggest a construction of a simple convex polytope, called graph-associahedra, which is associated with a given graph \(\Gamma\) and whose face partial order coincides with the partial order of sets of connected subgraphs of \(\Gamma\). This construction includes as particular cases the Stasheff associahedron and the Bott-Taubes cyclohedron. In case of simplicial Coxeter groups and respective Coxeter complexes the graph-associahedron represents its fundamental domain. Furthermore, the minimal blow-ups of such Coxeter complexes have tiling by graph-associahedra, which can be viewed as a generalization of the Deligne-Knudsen-Mumford compactification of the real moduli space of rational curves with marked points.

MSC:
52B05 Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.)
05B45 Combinatorial aspects of tessellation and tiling problems
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
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