## Sperner Theorem on Maximal Antichains

Let \(S\) be a family of subsets of \(\{1,\ldots,n\}\) such that no set in \(S\) contains another. This is often called an antichain. Theorem. [Sperner’s Theorem] \[ |S| \leq {n \choose \lfloor n/2 \rfloor}. \] The proof of Sperner’s Theorem …