counting theorem

Given a group action of a finite group $G$ on a finite set $X$, the following expression gives the number of distinct orbits

 $\frac{1}{|G|}\sum_{g\in G}\operatorname{stab}_{g}(X)$

Where $\operatorname{stab}_{g}(X)$ is the number of elements fixed by the action of $g$.

Title counting theorem CountingTheorem 2013-03-22 12:22:23 2013-03-22 12:22:23 mathcam (2727) mathcam (2727) 12 mathcam (2727) Theorem msc 20M30 Cauchy-Frobenius-Burnside formula