For most of the basic inequalities in mathematics we know conditions which completely specify the cases of equality. Many combinatorial correlation inequalities are special cases of the AD-inequality, as explained in [3, 8, 10]. However, for this inequality it seems to be difficult to classify the cases of equality. Certainly this is even more difficult for the much more general inequalities of [3] and its relatives, which can be produced by the very same ideas of exploiting notions of expansiveness. In fact, the equality characterization problem for these general inequalities constitutes by itself a rich area in combinatorial extremal theory. Closer to home there are the equality characterization problems for inequalities, which are consequences of the AD-inequality. Aharoni and Holzman [1] completely settled this for the Marica-SchOnheim inequality. Another, though fairly special, still interesting case of AD could be handled by Beck [17]. It seems that the first study of this kind was made by Daykin, Kleitman and West [12], who investigated the inequality