Combinatorial Necklaces and Bracelets

A combinatorial necklace is a circle of n coloured beads, with up to k different colours.

If we think of a necklace as a string of n characters from an alphabet of size k, we can say that two strings are equivalent if one can be rotated to be the same as the other i.e. aabb = abba = bbaa = baab.

A bracelet is a necklace that can be turned over i.e. strings are equivalent under reversal e.g. abcd = dcba.

Below you can see all unique necklaces or bracelets given n and k.


Further Reading