The method of double chains for largest families with excluded subposets

Details The method of double chains for largest families with excluded subposets The method of double chains for largest families with excluded subposets

2012-04-24

arxiv.org/abs/1204.5355v1

Mathematics

Combinatorics

8 pages, 5 figures. Submitted to The Electronic Journal of Graph Theory and Applications (EJGTA)

Scientific paper

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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