Cyclic permutations and nearly symmetric integer vectors

AbstractGiven an integer vector xT=(x1,…,xn) with the property x1>x2>⋯ >xn>0, it is shown that the convex hull of the n cyclic permutations of x contains all the nearly symmetric integer vectors majorized by x. A generalization to noninteger vectors and an application to a class of integer symmetric optimization problems are also given