A result on rearrangements

Circular symmetry is defined for ordered sets ofn real numbers: (y)=(y ₁,...,y _n). Letf(x) be non-decreasing and convex forx≧0 and let (y) be given except in arrangement. The Σ _i ⁼¹ⁿ f(|y _i−y _i+1|) (wherey _n+1=y ₁) is minimal if (and under some additional assumptions only if) (y) is arranged in circular symmetrical order. Sponsored by the Mathematics Research Center, United States Army under Contract No. DA-11-022-ORD-2059, University of Wisconsin, Madison.