http://openproblemgarden.org/op/extension_complexity_of_convex_polygons Comments for "Extension complexity of (convex) polygons" en http://openproblemgarden.org/op/extension_complexity_of_convex_polygons <table cellspacing="10"> <tr> <td> Author(s): <a href="/kpz_equation_central_limit_theorem"></a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/geometry">Geometry</a> » <a href="/category/polytopes">Polytopes</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <p>The extension complexity of a polytope <img class="teximage" src="/files/tex/b2b0b759db4d5a1b3204c38cdee6d9bd9e0d0dab.png" alt="$ P $" /> is the minimum number <img class="teximage" src="/files/tex/0f3b87f25409a259a157fcac9808cafa54efa0c7.png" alt="$ q $" /> for which there exists a polytope <img class="teximage" src="/files/tex/a797ac307899650a86e60bca713799dc723ca31a.png" alt="$ Q $" /> with <img class="teximage" src="/files/tex/0f3b87f25409a259a157fcac9808cafa54efa0c7.png" alt="$ q $" /> facets and an affine mapping <img class="teximage" src="/files/tex/d50751807ed5c1d6dc4d2f5a7db430b0423e9633.png" alt="$ \pi $" /> with <img class="teximage" src="/files/tex/2e9761bb227dc9bd3f6300f2bf729ea56f871b0d.png" alt="$ \pi(Q) = P $" />.</p> <div class="envtheorem"><b>Question</b>&nbsp;&nbsp; Does there exists, for infinitely many integers <img class="teximage" src="/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png" alt="$ n $" />, a convex polygon on <img class="teximage" src="/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png" alt="$ n $" /> vertices whose extension complexity is <img class="teximage" src="/files/tex/a73a961afec6ce1f7ee7b7db81e0dd55ba54d187.png" alt="$ \Omega(n) $" />? </div> </tr></td> </table> </td> </tr> </table> polytope, projection, extension complexity, convex polygon Geometry Polytopes http://openproblemgarden.org/op/extension_complexity_of_convex_polygons#comment Sat, 13 Aug 2011 18:09:51 +0200 DOT 37341 at http://openproblemgarden.org