http://openproblemgarden.org/op/the_alon_tarsi_basis_conjecture Comments for "The Alon-Tarsi basis conjecture" en http://openproblemgarden.org/op/the_alon_tarsi_basis_conjecture <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/alon">Alon</a>; <a href="/category/linial">Linial</a>; <a href="/category/meshulam">Meshulam</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; If <img class="teximage" src="/files/tex/d7626d3626b2054ebc198940785a7861d2fae9c2.png" alt="$ B_1,B_2,\ldots B_p $" /> are invertible <img class="teximage" src="/files/tex/fd981d449b91b1f4889d87406e6aa7d8acfb5d68.png" alt="$ n \times n $" /> matrices with entries in <img class="teximage" src="/files/tex/e8c94ceb5a9d688bff114c12f7fe9fe47ef955fc.png" alt="$ {\mathbb Z}_p $" /> for a prime <img class="teximage" src="/files/tex/928cd9d544fdea62f88a627aaee28c416c4366c0.png" alt="$ p $" />, then there is a <img class="teximage" src="/files/tex/18102393d42ad781eb0253bf9bee94b60757ed23.png" alt="$ n \times (p-1)n $" /> submatrix <img class="teximage" src="/files/tex/7a8d9782350e8eb5a84c149576d83160492cbdd3.png" alt="$ A $" /> of <img class="teximage" src="/files/tex/86661dc2948aeca789b4392c2e2a9cbf7d96f735.png" alt="$ [B_1 B_2 \ldots B_p] $" /> so that <img class="teximage" src="/files/tex/7a8d9782350e8eb5a84c149576d83160492cbdd3.png" alt="$ A $" /> is an AT-base. </div> </tr></td> </table> </td> </tr> </table> Alon, Noga Linial, Nathan Meshulam, Roy additive basis matrix Combinatorics Matrices http://openproblemgarden.org/op/the_alon_tarsi_basis_conjecture#comment Thu, 08 Mar 2007 14:01:19 +0100 mdevos 152 at http://openproblemgarden.org