Optimizing the Incidences between Points and Arcs on a Circle
Abstract
Given a set P of 2n+1 points regularly spaced on a circle, a number pi for pairwise distinct points and a number alpha for pairwise distinct and fixed length arcs incident to points in P, the sum of incidences between alpha arcs and pi points, is optimized by contiguously assigning both arcs and points. An extension to negative incidences by considering $\pm 1$ weights on points is provided. Optimizing a special case of a bilinear form (Hardy, Littlewood and Pólya' theorem) as well as Circulant $\times$ anti-Monge QAP directly follow.