Do you know if there exist algebraic studies of the ring of the power series which emerge when using the theory of Polya for enumeration of sets with certain symmetries? For instance if some ideals have nice properties, and similar.


I have seen a brief account in the chapter "Algebraic Enumeration" by Gessel and Stanley in the "Handbook of Combinatorics," but not much more. 



Polya's theory of counting and commutative algebra
Pólya's theorem arises in the theory of invariants of finite groups. See Section 10 of <http://math.mit.edu/~rstan/pubs/pubfiles/38.pdf>.


