Consider the unit circle S1 with distance function d measured along the circle. We show that for every selection of 2n points x1,⋯,xn,y1, ⋯,yn∈S1 there exists i∈1,⋯,n such that ∑k=1nd(xi,xk)≤∑k=1nd(xi,yk). We also discuss a game theoretic interpretation of this result.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Game theory