counting theorem

Given a group actionMathworldPlanetmath of a finite groupMathworldPlanetmath G on a finite setMathworldPlanetmath X, the following expression gives the number of distinct orbits


Where stabg(X) is the number of elements fixed by the action of g.

Title counting theorem
Canonical name CountingTheorem
Date of creation 2013-03-22 12:22:23
Last modified on 2013-03-22 12:22:23
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 12
Author mathcam (2727)
Entry type Theorem
Classification msc 20M30
Synonym Cauchy-Frobenius-Burnside formula