Abstract
Given a convex cone C in Rd, an integral zonotope T is the sum of segments [0,vi] (i=1,…,m) where each vi∈C is a vector with integer coordinates. The endpoint of T is k=∑1mvi. Let T(C,k) be the family of all integral zonotopes in C whose endpoint is k∈C. We prove that, for large k, the zonotopes in T(C,k) have a limit shape, meaning that, after suitable scaling, the overwhelming majority of the zonotopes in T(C,k) are very close to a fixed convex set. We also establish several combinatorial properties of a typical zonotope in T(C,k).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
