by Bey, Ch..

**Series:** 2003-37, Preprints

- MSC:
- 05C35 Extremal problems
- 05C65 Hypergraphs

**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 a new and short proof of the Ahlswede-Katona result.

**Keywords:**

Isoperimetric Problem, Kleitman West Problem, Hypergraph