Math
Counting necklaces: Burnside's lemma
Count necklaces and bracelets with Burnside’s lemma, inspect symmetry operations and verify the result by enumerating representatives.
Try this
Rotations identify necklaces; adding reflections identifies bracelets. Burnside counts fixed colourings from permutation cycles and averages over the group. An independent enumeration finds canonical representatives. Click a bead on the left to recolour it.
Equations used in the module
Equations Number of orbits = (1/|G|) Σg∈G |Fix(g)| A permutation with c cycles fixes kᶜ colourings A rotation by r places has gcd(n,r) cycles Rotations: |G|=n; rotations and reflections: |G|=2n
