Set families with a forbidden induced subposet

Edward Boehnlein; Tao Jiang

Set families with a forbidden induced subposet

Combinatorics 2011-06-14 v1

Authors: Edward Boehnlein , Tao Jiang

Abstract

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.

Keywords

set families forbidden induced subposet Hasse diagram tree poset asymptotic size Sperner's theorem

Cite

@article{arxiv.1106.2315,
  title  = {Set families with a forbidden induced subposet},
  author = {Edward Boehnlein and Tao Jiang},
  journal= {arXiv preprint arXiv:1106.2315},
  year   = {2011}
}

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