Set families with a forbidden induced subposet

Details Set families with a forbidden induced subposet Set families with a forbidden induced subposet

2011-06-12

arxiv.org/abs/1106.2315v1

Mathematics

Combinatorics

Scientific paper

For each poset $H$ whose Hasse diagram is a tree of height $k$, we show that
the largest size of a family $\cF$ of subsets of $[n]=\{1,..., n\}$ not
containing $H$ as an induced subposet is asymptotic to $(k-1){n\choose
\fl{n/2}}$. This extends the result of Bukh \cite{bukh}, which in turn
generalizes several known results including Sperner's theorem.

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