

























What is the smallest size of a family of subsets of $[n]$ such that it does not contain an induced copy of $Q_2$ as a poset (known as the \textit{diamond}), but adding a new set creates such a copy? It is easy to see that a maximal chain has this property, and thus the answer is at most $n+1$. Despite the simplicity of the diamond structure, the lower bound stagnated at $\sqrt n$ for quite some time, until recently the authors obtained a linear lower bound. In this paper, we fully solve this question showing that such a family must have size at least $n+1$.
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。