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The Erdős-Szekeres theorem and congruences

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Abstract

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.

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Authors and Affiliations

  1. Steklov Mathematical Institute, Steklov, Russia

    V. A. Koshelev

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  1. V. A. Koshelev
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Original Russian Text © V. A. Koshelev, 2010, published in Matematicheskie Zametki, 2010, Vol. 87, No. 4, pp. 572–579.

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Koshelev, V.A. The Erdős-Szekeres theorem and congruences. Math Notes 87, 537–542 (2010). https://doi.org/10.1134/S0001434610030314

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  • DOI: https://doi.org/10.1134/S0001434610030314

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