Maximum antichains in random subsets of a finite set
This nice paper investigates the maximum antichains in random subsets of a finite set, taking every subset independently with probability \(p.\) The main result states: if \(pn/\log n \rightarrow \infty\) then the analogue of the Sperner theorem holds, namely the biggest antichain out of those random subsets is formed almost surely by all chosen subsets of size \(\lfloor n/2\rfloor \). This is almost surely not the case if \(pn \not\rightarrow \infty.\)
scientific article; zbMATH DE number 1474639