The complexity of combinatorial isomorphism problems

Deciding isomorphism of balanced incomplete block designs is polynomial time equivalent to deciding graph isomorphism or isomorphism complete. Deciding isomorphism of (r, λ)-systems, exact set packings, pairwise balanced designs, and partially balanced incomplete block designs are all isomorphism complete problems. Isomorphism of exact set packings is isomorphism complete, isomorphism of pairwise balanced incomplete block designs (PBIBD's) is isomorphism complete, isomorphism of pairwise balanced designs (PBD's) is isomorphism complete, and balanced incomplete block designs (BIBD) isomorphism is isomorphism complete.