%0 Journal Article
%T The method of double chains for largest families with excluded subposets
%A Peter Burcsi
%A Daniel T. Nagy
%J Electronic Journal of Graph Theory and Applications
%D 2013
%I Indonesian Combinatorial Society (InaCombS), Graph Theory and Applications (GTA) Research Centre, The University of Newcastle, Australia, Institut Teknologi Bandung (ITB), Indonesia
%X For a given finite poset $P$, $La(n,P)$ denotes the largest size of a family $mathcal{F}$ of subsets of $[n]$ not containing $P$ as a weak subposet. We exactly determine $La(n,P)$ for infinitely many $P$ posets. These posets are built from seven base posets using two operations. For arbitrary posets, an upper bound is given for $La(n,P)$ depending on $|P|$ and the size of the longest chain in $P$. To prove these theorems we introduce a new method, counting the intersections of $mathcal{F}$ with double chains, rather than chains.
%U http://ejgta.org/index.php/ejgta/article/view/17