118 citations · 220 across the 30 of their papers we have counts for
12 papers · 1 filter
Small kissing polytopes
Antoine Deza, Zhongyuan Liu, Lionel Pournin
A lattice -polytope is the convex hull of a set of points in whose coordinates are integers ranging between and . We consider the smallest possible dis…
The expansion of half-integral polytopes
Jean Cardinal, Lionel Pournin
The expansion of a polytope is an important parameter for the analysis of the random walks on its graph. A conjecture of Mihai and Vazirani states that all -polytopes have exp…
The rotation distance of brooms
Jean Cardinal, Lionel Pournin, Mario Valencia-Pabon
The associahedron of a graph has the property that its vertices can be thought of as the search trees on and its edges as the rotations between two search…
Sizing the White Whale
Antoine Deza, Mingfei Hao, Lionel Pournin
We propose a computational, convex hull free framework that takes advantage of the combinatorial structure of a zonotope, as for example its symmetry group, to orbitwise generate a…
Diameter estimates for graph associahedra
Jean Cardinal, Lionel Pournin, Mario Valencia-Pabon
Graph associahedra are generalized permutohedra arising as special cases of nestohedra and hypergraphic polytopes. The graph associahedron of a graph encodes the combinatorics…
Primitive point packing
Antoine Deza, Lionel Pournin
A point in the -dimensional integer lattice is primitive when its coordinates are relatively prime. Two primitive points are multiples of one another when they ar…
A linear optimization oracle for zonotope computation
Antoine Deza, Lionel Pournin
A class of counting problems ask for the number of regions of a central hyperplane arrangement. By duality, this is the same as counting the vertices of a zonotope. We give several…
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…
Eccentricities in the flip-graphs of convex polygons
Lionel Pournin
The flip-graph of a convex polygon is the graph whose vertices are the triangulations of and whose edges correspond to flips between them. The eccentricity of a triangulati…
Once punctured disks, non-convex polygons, and pointihedra
Hugo Parlier, Lionel Pournin
We explore several families of flip-graphs, all related to polygons or punctured polygons. In particular, we consider the topological flip-graphs of once-punctured polygons which,…
The asymptotic diameter of cyclohedra
Lionel Pournin
It is shown here that the diameter of the -dimensional cyclohedron is not greater than . It is also shown that the coefficient in this upper bound is…
The diameter of associahedra
Lionel Pournin
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…