Ideas for an Old Analytic Enigma about the Sphere that Fail in Intriguing Ways
Frederik von Heymann · 2010
For any given dimension n and unit vector a 2 S n 1 , we investigate the well known question of how many sign vectors in {±1} n can have a scalar product with a between 1 and 1. We look at reformulations of this, and use simple observations about a geometric version of the question to derive an algorithm that finds unit vectors maximizing this number for given dimension. Our results support the conjectured lower bound of 1/2 of the sign vectors.