  We extend the discrete majorization theory by working with non-normalized
Lorenz curves. Then we prove two generalizations of the Muirhead theorem. These
not only use elementary transfers but also local increases. Together these
operations are described as elementary impact increases. The first
generalization shows that if an array X is dominated, in the generalized sense,
by an array Y then Y can be derived from X by a finite number of elementary
impact increases and this in such a way that each step transforms an array into
a new one which is strictly larger in the generalized majorization sense. The
other one shows that if the dominating array, Y, is ordered decreasingly then
elementary impact increases starting from the dominated array, X, lead to the
dominating one. Here each step transforms an array to a new one for which the
decreasingly ordered version dominates the previous one and is dominated by Y.
