Lubell mass and induced partially ordered sets

Abstract

We prove that for every partially ordered set $P$, there exists $c(P)$ such that every family $\mathcal{F}$ of subsets of $[n]$ ordered by inclusion and which contains no induced copy of $P$ satisfies ${\sum }_{F\in \mathcal{F}}1/\left(\genfrac{}{}{0ex}{}{n}{|F|}\right)\le c(P)$. This confirms a conjecture of Lu and Milans.

18 pages

References in corpus (1)

• Set families with forbidden subposets