## Ceballos, C. and Manneville, T. and Pilaud, V. and Pournin, L. - Diameters and geodesic properties of generalizations of the associahedron

dmtcs:2540 - Discrete Mathematics & Theoretical Computer Science, January 1, 2015, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Diameters and geodesic properties of generalizations of the associahedron

Authors: Ceballos, C. and Manneville, T. and Pilaud, V. and Pournin, L.

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.

Volume: DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Section: Proceedings
Published on: January 1, 2015
Submitted on: November 21, 2016
Keywords: flip graph diameter,non-leaving-face property,generalized associahedra,graph associahedra,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]