The diameter of associahedra |
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Authors: | Lionel Pournin |
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Institution: | 1. LIAFA, Université Paris Diderot, Case 7014, 75205 Paris Cedex 13, France;2. EFREI, 30-32 avenue de la République, 94800 Villejuif, France |
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Abstract: | It is proven here that the diameter of the d -dimensional associahedron is 2d−4 when d is greater than 9. Two maximally distant vertices of this polytope are explicitly described as triangulations of a convex polygon, and their distance is obtained using combinatorial arguments. This settles two problems posed about twenty-five years ago by Daniel Sleator, Robert Tarjan, and William Thurston. |
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Keywords: | Triangulations Flip-graphs |
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