http://openproblemgarden.org/op/rotas_unimodal_conjecture Comments for "Rota's unimodal conjecture" en http://openproblemgarden.org/op/rotas_unimodal_conjecture <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/rota_gian_carlo">Rota</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/combinatorics">Combinatorics</a> » <a href="/category/matroid_theory">Matroid Theory</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <p>Let <img class="teximage" src="/files/tex/3f02401f624e31ef8679d3c3628c1f310058f388.png" alt="$ M $" /> be a matroid of rank <img class="teximage" src="/files/tex/535dee6c3b72bcc4d571239ed00be162ee1e6fbe.png" alt="$ r $" />, and for <img class="teximage" src="/files/tex/6864d307c3d858e262df009fbc956d296b82dc70.png" alt="$ 0 \le i \le r $" /> let <img class="teximage" src="/files/tex/05a87be73e5273461a2280f88efbd1cc24810d1b.png" alt="$ w_i $" /> be the number of closed sets of rank <img class="teximage" src="/files/tex/ca49c241ece07915c97a31774a977841c6f0414c.png" alt="$ i $" />.</p> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; <img class="teximage" src="/files/tex/44d0d863f1306476a87d39f7b389e116afd6410d.png" alt="$ w_0,w_1,\ldots,w_r $" /> is unimodal. </div> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; <img class="teximage" src="/files/tex/44d0d863f1306476a87d39f7b389e116afd6410d.png" alt="$ w_0,w_1,\ldots,w_r $" /> is log-concave. </div> </tr></td> </table> </td> </tr> </table> Rota, Gian-Carlo flat log-concave matroid Combinatorics Matroid Theory http://openproblemgarden.org/op/rotas_unimodal_conjecture#comment Fri, 08 Jun 2007 06:55:57 +0200 mdevos 361 at http://openproblemgarden.org