"Enumerative problems in framework of group action orthogonality"
The count of orbits of a group acting on a set may be facilitated
considerably by knowledge of another action orthogonal to the first
one. (Two group actions are called mutually orthogonal if any
non-identity element has a fixed point in at most one of them.)
This opportunity is characteristic for various combinatorial,
topological and algebraic objects which can be modelled by
transitive tuples of permutations. Numerous open problems are
posed and discussed.