Pólya Enumeration Theorem
A very general theorem that allows the number of discrete combinatorial objects of a given type to be enumerated (counted) as a function of their "order."
The most common application is in the counting of the number of simple
graphs of 
nodes, tournaments
on 
nodes, trees
and rooted trees with 
branches, groups
of order 
, etc. The theorem is an extension of
the Cauchy-Frobenius lemma, which is sometimes
also called Burnside's lemma, the Pólya-Burnside lemma, the Cauchy-Frobenius
lemma, or even "the lemma that is not Burnside's!"
Pólya enumeration is implemented as OrbitInventory[ci, x, w] in the Wolfram Language package Combinatorica` .
Contact the MathWorld Team
pólya enumeration
theorem
