Geodesic
The Erd\H{o}s--Szekeres Theorem and Congruences
Matematičeskie zametki, Tome 87 (2010) no. 4, pp. 572-579.

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The following problem of combinatorial geometry is considered. Given positive integers $n$ and $q$, find or estimate a minimal number $h$ for which any set of $h$ points in general position in the plane contains $n$ vertices of a convex polygon for which the number of interior points is divisible by $q$. For a wide range of parameters, the existing bound for $h$ is dramatically improved.
Keywords: Erdős–Szekeres problem, Erdős–Szekeres theorem, Ramsey theory.
Mots-clés : convex polygon, points in convex position 
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V. A. Koshelev. The Erd\H{o}s--Szekeres Theorem and Congruences. Matematičeskie zametki, Tome 87 (2010) no. 4, pp. 572-579. http://geodesic.mathdoc.fr/item/MZM_2010_87_4_a8/

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