03-37
Remarks on an edge isoperimetric problem
by Bey, Ch.
Preprint series: 03-37, Preprints
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
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