KnowraSperner's theoremLinked fromLinked fromThe 3 pages that link to Sperner's theorem, each with the reason it gives.All 3Related 3Extremal combinatoricsRelated: It solves a fundamental maximum-size problem for families ordered by containment.AntichainRelated: It gives the exact maximum antichain size in the subset-inclusion order.Erdős–Szekeres theorem (monotone subsequences)Related: It studies a different extremal constraint on order, rather than monotone subsequences in a linear sequence.