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Discrete Mathematics & Theoretical Computer Science |
The $n$-dimensional associahedron is a polytope whose vertices correspond to triangulations of a convex $(n + 3)$-gon and whose edges are flips between them. It was recently shown that the diameter of this polytope is $2n - 4$ as soon as $n > 9$. We study the diameters of the graphs of relevant generalizations of the associahedron: on the one hand the generalized associahedra arising from cluster algebras, and on the other hand the graph associahedra and nestohedra. Related to the diameter, we investigate the non-leaving-face property for these polytopes, which asserts that every geodesic connecting two vertices in the graph of the polytope stays in the minimal face containing both.
Source : ScholeXplorer
IsRelatedTo ARXIV 1803.11427 Source : ScholeXplorer IsRelatedTo DOI 10.37236/7762 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.1803.11427
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