Extensions and Shadows (14)

We now show Theorem 2.3: \( \kappa[Shd(\mathcal{F}, r)] < \frac{4 r}{m} \kappa(\mathcal{F}) + \frac{m^2}{n} \) for any \( m \in [\epsilon n] \) and \( r \in [m] \). Link to: 6/22/23 Like we saw on 7/21/25, the theorem means that the \( r \)-shadow is a vast majority of \( {X \choose r} \) […]