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.

**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.

© 1996-9

1999-05-25