3 papers
math.CO2019
The diameter of lattice zonotopes
Antoine Deza, Lionel Pournin, Noriyoshi Sukegawa
We establish sharp asymptotic estimates for the diameter of primitive zonotopes when their dimension is fixed. We also prove that, for infinitely many integers , the largest pos…
math.MG2018
Elementary moves on lattice polytopes
Julien David, Lionel Pournin, Rado Rakotonarivo
We introduce a graph structure on Euclidean polytopes. The vertices of this graph are the -dimensional polytopes contained in and its edges connect any two polyto…
math.MG2018
Diameter, decomposability, and Minkowski sums of polytopes
Antoine Deza, Lionel Pournin
We investigate how the Minkowski sum of two polytopes affects their graph and, in particular, their diameter. We show that the diameter of the Minkowski sum is bounded below by the…