http://garden.irmacs.sfu.ca/op/saturated_k_sperner_systems_of_minimum_size Comments for "Saturated $k$-Sperner Systems of Minimum Size" en http://garden.irmacs.sfu.ca/op/saturated_k_sperner_systems_of_minimum_size <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/morrison_natasha">Morrison</a>; <a href="/category/noel_jonathan_a">Noel</a>; <a href="/category/scott_alex">Scott</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/combinatorics">Combinatorics</a> » <a href="/category/posets">Posets</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <div class="envtheorem"><b>Question</b>&nbsp;&nbsp; Does there exist a constant <img class="teximage" src="/files/tex/71b371b57345af0cbcfd2ffd78362b8988723a7d.png" alt="$ c&gt;1/2 $" /> and a function <img class="teximage" src="/files/tex/77717a7ba8441af96e47411a5b9a5d4a913f3dba.png" alt="$ n_0(k) $" /> such that if <img class="teximage" src="/files/tex/e6c6b51d4e2df6fd85840bc289e38c981674e057.png" alt="$ |X|\geq n_0(k) $" />, then every saturated <img class="teximage" src="/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png" alt="$ k $" />-Sperner system <img class="teximage" src="/files/tex/cb32025ab3209d1516fd6ea63a4d8eb206a81411.png" alt="$ \mathcal{F}\subseteq \mathcal{P}(X) $" /> has cardinality at least <img class="teximage" src="/files/tex/1564812bc34ed3ebd060debb561be85acfb45f10.png" alt="$ 2^{(1+o(1))ck} $" />? </div> </tr></td> </table> </td> </tr> </table> Morrison, Natasha Noel, Jonathan A. Scott, Alex antichain extremal combinatorics minimum saturation saturation Sperner system Combinatorics Posets http://garden.irmacs.sfu.ca/op/saturated_k_sperner_systems_of_minimum_size#comment Sat, 12 Apr 2014 17:19:02 +0200 Jon Noel 59928 at http://garden.irmacs.sfu.ca