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The method of double chains for largest families with excluded subposets

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Author(s): Peter Burcsi | Daniel T. Nagy

Journal: Electronic Journal of Graph Theory and Applications
ISSN 2338-2287

Volume: 1;
Issue: 1;
Date: 2013;
Original page

Keywords: excluded subposet | Lubell’s function | double chain

ABSTRACT
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.
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