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On the Positive Fraction Erdos--Szekeres Theorem for Convex Sets

Publication at Faculty of Mathematics and Physics |
2006

Abstract

We show that for any $F$ in general position there is a $k$-cluster $F' \subset F$ of size at least $2^{-37.8k-o(1)}|\F|$. This improves the result of Pach and Solymosi.