http://openproblemgarden.org/op/rotas_basis_conjecture Comments for "Rota's basis conjecture" en http://openproblemgarden.org/op/rotas_basis_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/matrices">Matrices</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; Let <img class="teximage" src="/files/tex/517af4139f21bb21424f7896561555919bc4678a.png" alt="$ V $" /> be a vector space of dimension <img class="teximage" src="/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png" alt="$ n $" /> and let <img class="teximage" src="/files/tex/291e2c3146a88c4c126a456a784d77be3cf9266f.png" alt="$ B_1,\ldots,B_n \subseteq V $" /> be bases. Then there exist <img class="teximage" src="/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png" alt="$ n $" /> disjoint transversals of <img class="teximage" src="/files/tex/49d7d4d20a702d358d1660e3a717da670170a011.png" alt="$ B_1,\ldots,B_n $" /> each of which is a base. </div> </tr></td> </table> </td> </tr> </table> Rota, Gian-Carlo base latin square linear algebra matroid transversal Combinatorics Matrices http://openproblemgarden.org/op/rotas_basis_conjecture#comment Sat, 06 Oct 2007 06:59:18 +0200 mdevos 631 at http://openproblemgarden.org