19 Apr '06 16:15

This is the general case of something relatively easy, but presumably it involves a lot of legwork.

Given n beads and some partition of {1,2,...n} into m subsets of size k(1), k(2),...k(m), let the beads of each subset be given a different colour (ie, we have k(1) white beads, k(2) yellow ones, etc). How many essentially different necklaces (arrangement of beads in a circle) are possible?

Given n beads and some partition of {1,2,...n} into m subsets of size k(1), k(2),...k(m), let the beads of each subset be given a different colour (ie, we have k(1) white beads, k(2) yellow ones, etc). How many essentially different necklaces (arrangement of beads in a circle) are possible?