An improved bound on the diamond-free poset problem

Abstract

In the theory of partially-ordered sets, the two-dimensional Boolean lattice is known as the diamond. In this paper, we show that, if $\mathcal{F}$ is a family in the $n$-dimensional Boolean lattice that has no diamond as a subposet, then $|\mathcal{F}|\le 2.206653\left(\genfrac{}{}{0ex}{}{n}{\lfloor n/2\rfloor }\right)$, improving a bound by the authors and Michael Young.

The paper has been withdrawn. There is an irreparable error in Lemma 9

References in corpus (1)

• On crown-free families of subsets