KnowraErdős–Szekeres theorem (monotone subsequences)Linked fromLinked fromThe 3 pages that link to Erdős–Szekeres theorem (monotone subsequences), each with the reason it gives.All 3Related 3Pigeonhole principleRelated: Its proof assigns pairs of subsequence lengths and uses the principle to show those pairs cannot repeat.Ramsey theoryRelated: It is a classic sequence result with a Ramsey-style guarantee of order.Dilworth's theoremRelated: Its subsequence conclusion follows from chain and antichain reasoning on sequence positions.