http://openproblemgarden.org/op/davenports_constant Comments for "Davenport's constant" en http://openproblemgarden.org/op/davenports_constant <table cellspacing="10"> <tr> <td> Author(s): <a href="/kpz_equation_central_limit_theorem"></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>For a finite (additive) abelian group <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" />, the <em>Davenport constant</em> of <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" />, denoted <img class="teximage" src="/files/tex/675f61728ff327c6b49de455369ebc2a34b64ebb.png" alt="$ s(G) $" />, is the smallest integer <img class="teximage" src="/files/tex/4761b031c89840e8cd2cda5b53fbc90c308530f3.png" alt="$ t $" /> so that every sequence of elements of <img class="teximage" src="/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png" alt="$ G $" /> with length <img class="teximage" src="/files/tex/42014904948ca20e097b6d38933fa9096c796cad.png" alt="$ \ge t $" /> has a nontrivial subsequence which sums to zero.</p> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; <img class="teximage" src="/files/tex/2bea401874dc0a9cd37e10b6df927b12a7ce2402.png" alt="$ s( {\mathbb Z}_n^d) = d(n-1) + 1 $" /> </div> </tr></td> </table> </td> </tr> </table> Davenport constant subsequence sum zero sum Number Theory Combinatorial Number Theory http://openproblemgarden.org/op/davenports_constant#comment Sat, 08 Sep 2007 10:59:17 +0200 mdevos 563 at http://openproblemgarden.org