Suppose , , and , ..., is a sequence of real numbers. Then this sequence contains a monotonic increasing (decreasing) subsequence of terms or a monotonic decreasing (increasing) subsequence of terms. Dilworth's lemma is a generalization of this theorem.
See alsoCombinatorics, Dilworth's Lemma
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ReferencesHoffman, P. The Man Who Loved Only Numbers: The Story of Paul Erdős and the Search for Mathematical Truth. New York: Hyperion, pp. 54-55, 1998.
Referenced on Wolfram|AlphaErdős-Szekeres Theorem
Cite this as:
Weisstein, Eric W. "Erdős-Szekeres Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Erdos-SzekeresTheorem.html