Abstract
Among all collections of a given number of k-element subsets of an n-element groundset find a collection which maximizes the number of pairs of subsets which intersect in k–1 elements. This problem was solved for k=2 by Ahlswede and Katona, and is open for k>2. We survey some linear algebra approaches which yield to estimations for the maximum number of pairs, and we present another short proof of the Ahlswede-Katona result.
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