http://www.openproblemgarden.org/op/erdos_szekeres_conjecture Comments for "Erdös-Szekeres conjecture" en http://www.openproblemgarden.org/op/erdos_szekeres_conjecture#comment-6635 <p>Now true for n = 6 as well by computer-aided solution of Szekeres and Peters (2006).</p> Tue, 14 Apr 2009 07:23:17 +0200 Anonymous comment 6635 at http://www.openproblemgarden.org http://www.openproblemgarden.org/op/erdos_szekeres_conjecture <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/erdos">Erdos</a>; <a href="/category/szekeres">Szekeres</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/geometry">Geometry</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; Every set of <img class="teximage" src="/files/tex/78669eb6d8b95f5ad57efe25b8ed4f27b42cb6f6.png" alt="$ 2^{n-2} + 1 $" /> points in the plane in general position contains a subset of <img class="teximage" src="/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png" alt="$ n $" /> points which form a convex <img class="teximage" src="/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png" alt="$ n $" />-gon. </div> </tr></td> </table> </td> </tr> </table> Erdos, Paul Szekeres, George combinatorial geometry Convex Polygons ramsey theory Geometry http://www.openproblemgarden.org/op/erdos_szekeres_conjecture#comment Wed, 08 Oct 2008 06:48:14 +0200 mdevos 2400 at http://www.openproblemgarden.org