Abstract
AbstractThe classical Steinitz theorem states that if the origin belongs to the interior of the convex hull of a set , then there are at most points of whose convex hull contains the origin in the interior. Bárány, Katchalski, and Pach proved the following quantitative version of Steinitz's theorem. Let be a convex polytope in containing the standard Euclidean unit ball . Then there exist at most vertices of whose convex hull satisfies with . They conjectured that holds with a universal constant . We prove , the first polynomial lower bound on . Furthermore, we show that is not greater than .
Sign-in/Register to access full text options 
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.
