On the probability that subset sequences are minimal (Q1817583)

Let \([n]= \{1,2,\dots, n\}\) and let \(\omega= (\omega(i))^p_{i= 1}\) be a \(p\)-sequence of \(k\)-sets of \([n]\). If there is an element \(x_i\) in \(\omega(i)\) which is not in any other \(\omega(j)\) with \(j\neq i\), then \(x_i\) is called a representative of \(\omega(i)\). Further, if every entry of \(\omega\) has \(t\) representatives, then \(\omega\) is called \((n,p,k,t)\)-minimal. The authors give a lower bound for the probability that \(\omega\) is \((n,p,k,t)\)-minimal.