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On a Theorem of Erdös and Szekeres

Published online by Cambridge University Press:  20 November 2018

M.V. Subbarao
M.V. Subbarao*
Affiliation:
University of Missouri, University of Alberta
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Given a sequence of r distinct real numbers such that the number of terms of every decreasing subsequence is at most m, then there exists an increasing subsequence of more than n terms, where n is the largest integer less than r/m.

An extremely simple and elegant proof of the theorem was given by A. Seidenberg [2]. This note is intended to point out that a result analogous to the above holds under a more general setting.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 4 , October 1968 , pp. 597 - 598
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Erdös, P. and Szekeres, G., A combinatorial problem in geometry. Composite Math. 2 (1935) 463-470.Google Scholar
2. Seidenberg, A., A simple proof of a theorem of Erdös and Szekeres. J. London Math. Soc. 34 (1959) 352.Google Scholar