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Burnside's Lemma

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Let $G$ be a group acting on a set $X$. The number of orbits of $G$ on $X$ is equal to:

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A
The average number of elements in each orbit
💡 Explanation:

Burnside's Lemma states that the number of orbits of $G$ on $X$ is equal to the average number of elements in each orbit, which is given by the formula $\frac{1}{|G|} \sum_{g \in G} |X^g|$, where $X^g$ is the set of elements in $X$ that are fixed by $g$.

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