Maximum shattering

Noga Alon, Varun Sivashankar, Daniel G. Zhu

A family $\mathcal{F}$ of subsets of $[n]=\{1,2,\dots ,n\}$ shatters a set $A\subseteq [n]$ if for every $A^{\prime }\subseteq A$ there is an $F\in \mathcal{F}$ such that $F\cap A=A^{\prime }$.…