Necklace Combinatorics & Burnside's Lemma
Counting distinct necklaces under rotation — Burnside counts fixed points of group action
Beads n:
5
Colors k:
2
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Burnside's lemma: |X/G| = (1/|G|) Σ |Fix(g)|
For rotational necklaces: N(n,k) = (1/n) Σ_{d|n} φ(n/d)·k^d
All distinct necklaces (up to rotation):