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A very general theorem which 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 Graphs of 
nodes, Trees and Rooted Trees with branches, Groups
of order , etc. The theorem is an extension of Burnside's Lemma and is sometimes also called the
Pólya-Burnside Lemma.
See also Burnside's Lemma, Graph (Graph Theory), Group, Rooted Tree, Tree
References
Harary, F. ``The Number of Linear, Directed, Rooted, and Connected Graphs.'' Trans. Amer. Math. Soc. 78, 445-463, 1955.
Pólya, G. ``Kombinatorische Anzahlbestimmungen für Gruppen, Graphen, und chemische Verbindungen.'' Acta Math. 68, 145-254, 1937.