• 1 Alfréd Rényi Institute of Mathematics
• 2 Technical University of Berlin / Technische Universität Berlin

We consider an extremal problem on labelled directed trees and applications to database theory. Among others, we will show explicit keysystems on an underlying set of size $n$, that cannot be represented by a database of less than $2^{n(1-c\cdot \log \log n / \log n)}$ rows.