Towards characterizing equality in correlation inequalities

نویسندگان

  • Rudolf Ahlswede
  • Levon H. Khachatrian
چکیده

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

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عنوان ژورنال:
  • Eur. J. Comb.

دوره 16  شماره 

صفحات  -

تاریخ انتشار 1995