The diameter of associahedra

By Lionel Pournin. 2012

123 citations recorded by the source corpus.

Abstract It is proven here that the diameter of the d-dimensional associahedron is 2 d − 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.

Subfields: Computer Graphics and Computer-Aided Design, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ec09b4a5a8964c3f2536e9f0ec2f289c0a42a76e