The Cycle Method and Its Limits

• Gyula O. H. Katona
Chapter

Abstract

A powerful tool of extremal set theory, the cycle method is surveyed in the paper. It works, however only when the non-emptyness of the pairwise intersections of the members of the family is assumed. If these intersections have to be at least 2, the method fails: the celebrated Complete Intersection Theorem by Ahlswede and Khachatrian cannot be proved by this method. We show the reasons and some attempts to overcome the difficulties.

Keywords

Convex Hull Cyclic Permutation Steiner System Cycle Method Profile Vector
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