Type: Article

On a Helly-type question for central symmetry

Garber, Alexey, Roldán-Pensado, Edgardo;

Abstract:

We study a certain Helly-type question by Konrad Swanepoel. Assume that X is a set of points such that every k-subset of X is in centrally symmetric convex position, is it true that X must also be in centrally symmetric convex position? It is easy to see that this is false if k?5, but it may be true for sufficiently large k. We show that the statement is not true even when k=8, but k=6 is enough if X is a simple closed curve.