An Erdős--Trotter problem on antichains with multiplicity $r$ on each occurring level

Yixin He, Quanyu Tang

Fix an integer $r\ge 2$. For each $n$ we consider families $\mathcal{F}\subseteq 2^{[n]}$ that form an antichain and have the property that, for every $t$, if there exists $A\in\math…