http://openproblemgarden.org/op/limiting_subsequence_sums_in_z_n_x_z_n Comments for "Few subsequence sums in Z_n x Z_n" en http://openproblemgarden.org/op/limiting_subsequence_sums_in_z_n_x_z_n <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/bollobas">Bollobas</a>; <a href="/category/leader">Leader</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; For every <img class="teximage" src="/files/tex/3f439dde8bba9a34c4b73a7bf35d2ba2d600dd53.png" alt="$ 0 \le t \le n-1 $" />, the sequence in <img class="teximage" src="/files/tex/784102d74f41429c112d0dd6746a4ab9f1957afe.png" alt="$ {\mathbb Z}_n^2 $" /> consisting of <img class="teximage" src="/files/tex/da6174078cbeae6601684c08526200d9254caa11.png" alt="$ n-1 $" /> copes of <img class="teximage" src="/files/tex/02e6ed02ec9ede67b905b1ca3c64be3eb3c6f11b.png" alt="$ (1,0) $" /> and <img class="teximage" src="/files/tex/4761b031c89840e8cd2cda5b53fbc90c308530f3.png" alt="$ t $" /> copies of <img class="teximage" src="/files/tex/2f2f87361c58fc118cefb1ab5cb288a25e20007f.png" alt="$ (0,1) $" /> has the fewest number of distinct subsequence sums over all zero-free sequences from <img class="teximage" src="/files/tex/784102d74f41429c112d0dd6746a4ab9f1957afe.png" alt="$ {\mathbb Z}_n^2 $" /> of length <img class="teximage" src="/files/tex/26b23f9cc4119b690ed97ea8d21da62ec7899f64.png" alt="$ n-1+t $" />. </div> </tr></td> </table> </td> </tr> </table> Bollobas, Bela Leader, Imre subsequence sum zero sum Number Theory Combinatorial Number Theory http://openproblemgarden.org/op/limiting_subsequence_sums_in_z_n_x_z_n#comment Sat, 10 Mar 2007 16:39:19 +0100 mdevos 156 at http://openproblemgarden.org