INEQUALITIES ON WELL-DISTRIBUTED POINT SETS ON CIRCLES
Alexander Engström · 2007
ABSTRACT. The setting is a finite set P of points on the circumference of a circle, where all points are assigned non-negative real weights w(p). Let Pi be all subsets of P with i points and no two distinct points within a fixed distance d. We prove that W 2 k ≥ Wk+1Wk−1 where Wk = ∑ ∏ A∈Pi p∈A w(p). This is done by first extending a theorem by Chudnovsky and Seymour on roots of stable set polynomials of claw-free graphs.