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 
@article{MZM_2010_87_4_a8,
     author = {V. A. Koshelev},
     title = {The {Erd\H{o}s--Szekeres} {Theorem} and {Congruences}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {572--579},
     publisher = {mathdoc},
     volume = {87},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_87_4_a8/}
}
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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/