Elsevier

Discrete Mathematics

Volume 257, Issues 2–3, 28 November 2002, Pages 411-414
Discrete Mathematics

Intersecting families with minimum volume

with gratitude to Daniel J. Kleitman
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Abstract

We determine the minimum volume (sum of cardinalities) of an intersecting family of subsets of an n-set, given the size of the family, by solving a simple linear program. From this, we obtain a lower bound on the average size of the sets in an intersecting family. This answers a question of G.O.H. Katona, whose 60th birthday we celebrate with this result.

Keywords

Intersecting family of sets
Average set size
Linear program

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Research supported in part by NSF Grant DMS-0072187.