Given a finite group acting on a set of elements, the Pólya–Burnside enumeration theorem counts the number of elements of a given type as a function of their order.

In this Demonstration, a set of binary strings of a given length is acted upon by the group . The first component acts by word-reversing, while the second acts by bit‐wise negation. Rewriting rules and corresponding orbits are explicitly worked out for these reflections.

The number of orbits is for even and for odd .