Burnside's lemma
Let $G$ be a finite group that acts on a set $X$. For each $g$ in $G$ let $X^g$ denote the set of elements in $X$ that are fixed by $g$. Then the number of orbits $$|X/G| = \frac{1}{|G|} \sum_{g\in G} |X^g|.$$
Problems
- Necklace of Beads
- TheBeautifulBoard
- Magic Bracelet
- Lucy and the Flowers
- Sorting Machine
- Pizza Toppings
- Alphabet soup2
- Drum Decorator1
- Count the Necklaces
- Cube Coloring