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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Bey, C. (2006). Remarks on an Edge Isoperimetric Problem. In: Ahlswede, R., et al. General Theory of Information Transfer and Combinatorics. Lecture Notes in Computer Science, vol 4123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11889342_62
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DOI: https://doi.org/10.1007/11889342_62
Publisher Name: Springer, Berlin, Heidelberg
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