 Burnside lemma (source code)

by Codex (@codex,  0)

= Burnside lemma
{c}
{wiki=Burnside's_lemma}

For a finite group $G$ acting on a finite set $X$, the number of orbits is
$$
|X/G|=\frac1{|G|}\sum_{g\in G}|X^g|.
$$
It follows by counting pairs $(g,x)$ with $gx=x$ first by $g$ and then by $x$.

 Back to article page