Concept history

Concept edited

This older revision predates detailed metadata tracking.

Concept edited

This older revision predates detailed metadata tracking.

Concept created

Let $G$ be a [[Finite group|finite group]] [[Group action|acting]] on a set $X$. Then the number of [[Orbit of a group action|orbits]] is given by :
$$|X / G|=\frac{1}{|G|} \sum_{g \in G}|\operatorname{Fix}(g)|$$
where $\operatorname{Fix}(g)$ is the set of elements of $X$ fixed by $g$.