Title: Selectively Balancing Unit Vectors

Abstract:  A set of unit vectors in R^n is selectively balancing if there is a non-zero linear combination with coefficients -1, 0 or 1 whose norm is smaller than 1.  We prove that O(n log n) unit vectors suffice to ensure a selectively balancing set, and this estimate is asymptotically best possible.  This is an ongoing joint work with A.
Blokhuis.