Fusion schemes and partially balanced incomplete block designs

The notion of fusion in association schemes is developed and then applied to group schemes. It is shown that the association schemes derived in [1] and [4] are special cases of \(A\)-fused schemes of group schemes \(X(G)\), where \(G\) is abelian and \(A\) is a group of automorphisms of \(G\). It is then shown that these latter schemes give rise to PBIB designs under constructions identical to those found in [1] and [4].