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

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