by Bey, Ch..
Series: 2003-37, Preprints
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 a new and short proof of the Ahlswede-Katona result.
Isoperimetric Problem, Kleitman West Problem, Hypergraph