A survey of results on mandatory representation designs (Q2747176)

A pairwise balanced design is a pair \((V,\text{QTR}{\mathcal B})\) and a set \(K\) of integers, where \(\text{QTR}{\mathcal B} \) is a collection of subsets of \(V\) called blocks so that each pair of distinct elements of \(V\) occurs in a unique block, each block has as size an integer in \(K.\) If an additional condition is fulfilled, that to each \(k\in K\) there is a block of size \(k,\) then the design is called a mandatory representation design, an MRD. The paper surveys results on MRD's as well raises some open questions.