03-38
On cross intersecting families of sets
by Bey, Ch.
Preprint series: 03-38, Preprints
- MSC:
- 05D05 Extremal set theory
Abstract: 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 $\omega_\ell,\omega_k$.
Keywords: Intersection Theorem
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