A Survey of Results on Mandatory Representation Designs

A mandatory representation design MRD \((K; v)\) is a pairwise balanced design PBD \((K; v)\) in which for each \(k \in K\) there is at least one block in the design of size \(k\). The study of the mandatory representation designs is closely related to that of subdesigns in pairwise balanced designs. In this paper, we survey the known results on MRDs and pose some open questions.