Convex cones, integral zonotopes, limit shape

Imre Bárány (1, 2) , Julien Bureaux (3) , Ben Lund (4)

1 Department of Mathematics UCL
2 Alfréd Rényi Institute of Mathematics
3 MODAL'X - Modélisation aléatoire de Paris X
4 RU - Rutgers, The State University of New Jersey [New Brunswick]

This paper is about integral zonotopes. It is proven that large zonotopes in a convex cone have a limit shape, meaning that, after suitable scaling, the overwhelming majority of the zonotopes are very close to a fixed convex set. Several combinatorial properties of large zonotopes are established.

Mots clés: convex cones; integer partitions; integer zonotopes; limit shape

Domaines: Combinatoire [math.CO]; Probabilités [math.PR]

Imre Bárány, Julien Bureaux, Ben Lund. Convex cones, integral zonotopes, limit shape. 2016. ⟨hal-01384444⟩