An improved bound on the diamond-free poset problem

Lucas Kramer; Ryan R. Martin

An improved bound on the diamond-free poset problem

Combinatorics 2015-03-13 v2

Authors: Lucas Kramer , Ryan R. Martin

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 $|\mathcal{F}|\leq 2.206653{n\choose \lfloor n/2\rfloor}$ , improving a bound by the authors and Michael Young.

Cite

@article{arxiv.1503.00631,
  title  = {An improved bound on the diamond-free poset problem},
  author = {Lucas Kramer and Ryan R. Martin},
  journal= {arXiv preprint arXiv:1503.00631},
  year   = {2015}
}

Comments

The paper has been withdrawn.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

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