We have seen that the fact that we have defined a permutation group as the permutations of some specific set doesn’t preclude us from thinking of the elements of that group as permuting the elements o...We have seen that the fact that we have defined a permutation group as the permutations of some specific set doesn’t preclude us from thinking of the elements of that group as permuting the elements of some other set as well.
George Pólya and Robert Redfield independently developed a theory of generating functions that describe the action of a group G on colorings of a set S by a set T when we know the action of G on S. Pó...George Pólya and Robert Redfield independently developed a theory of generating functions that describe the action of a group G on colorings of a set S by a set T when we know the action of G on S. Pólya’s work on the subject is very accessible in its exposition, and so the subject has become popularly known as Pólya theory, though Pólya-Redfield theory would be a better name. In this section we develop the elements of this theory.