Three layer $Q_2$-free families in the Boolean lattice

Details Three layer $Q_2$-free families in the Boolean lattice Three layer $Q_2$-free families in the Boolean lattice

2011-08-22

arxiv.org/abs/1108.4373v1

Mathematics

Combinatorics

Scientific paper

We prove that the largest $Q_2$-free family of subsets of $[n]$ which
contains sets of at most three different sizes has at most $(3 + 2\sqrt {3})N/3
+ o(N) \approx 2.1547N + o(N)$ members, where $N = {n \choose {\lfloor n/2
\rfloor}}$. This improves an earlier bound of $2.207N + o(N)$ by Axenovich,
Manske, and Martin.

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