The metamorphosis of lambda-fold block designs with block size four into lambda-fold triple systems (Q697991)

A \(\lambda\)-fold triple system is called a metamorphosis of a \(\lambda\)-fold block design with block size \(4\) if it can be obtained by removing an element from each block and arranging the removed elements into triangles. The authors give a complete solution of the problem for which \(n\) and \(\lambda\) there exists a \(\lambda\)-fold block design of order \(n\) with block size \(4\) which has a metamorphosis into a \(\lambda\)-fold block triple system. It turns out that necessary simple divisibility conditions are sufficient as well.