Leírás
Balancing and anti-balancing unit vector sums is a classical question which dates back more than a century. The basic problem is the following. Given a set of vectors of norm 1 in the d-dimensional Euclidean space, can we assign signs to the vectors so that their sum becomes small (balancing) or large (ant-balancing)? We seek the best possible bounds. Besides surveying some results in this family, we will prove asymptotically sharp estimates on several anti-balancing problems. In some special cases, we will also determine the exact optimum. This is a joint work with B. González Merino (University of Murcia).