by Bey, Ch..

**Series:** 2003-38, 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