Abstract by Shawn Green
Extensions of the Power Group Enumeration Theorem
The Power Group Enumeration Theorem counts orbits of functions between finite sets with a group of permutations acting on the domain and co-domain simultaneously. However, it assumes a group structure of a direct product of two subgroups. In the case that the group is not a direct product of two subgroups, the orbits can still be counted systematically. Additionally, more information can be extracted about the different kinds of orbits produced.