In mathematics, Muirhead's inequality, named after Robert Franklin Muirhead, also known as the "bunching" method, generalizes the inequality of arithmetic and geometric means. For any real vector define the "a-mean" [a] of positive real numbers x1, ..., xn by where the sum extends over all permutations σ of { 1, ..., n }. When the elements of a are nonnegative integers, the a-mean can be equivalen