On comparability of structures

Abstract The problem of comparability of structures and functions defined on structures is considered following the early work of Muirhead (confined to integral parametrization) and more modern generalization of Karamata. The basis of such comparabilities is the set of inequalities which when satisfied permit one to establish a relative order (importance) of the structures or associated functions. Chemical illustrations are given for both, Muirhead and Karamata inequalities. It is outlined how to go beyond the partial ordering in such comparison when additional information on the trends among the parameters involved is available.