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On cross intersecting families of sets

by Bey, Ch..

Series: 2003-38, Preprints

05D05 Extremal set theory

A family $\cA$ of $\ell$-element sets and a family $\cB$ of $k$-element sets are cross-intersecting if every set from $\cA$ has a nonempty
intersection with every set from $\cB$. We compare two previously established inequalities each related to the maximization
of the product $|\cA|\,|\cB|$, and give a new and short proof for one of them. We also determine the maximum of
$|\cA|\,\omega_\ell+|\cB|\,\omega_k$ for arbitrary positive weights $\omega_\ell,\omega_k$.

Intersection Theorem