Necklace polynomial
In combinatorial mathematics, the necklace polynomial, or Moreau's necklace-counting function, introduced by C. Moreau (1872), counts the number of distinct necklaces of n {\displaystyle n} colored beads chosen out of k {\displaystyle k} available colors, arranged in a cycle. Unlike the usual problem of graph coloring, the necklaces are assumed to be aperiodic (not composed from a repeated subsequence), and counted up to rotation (rotating the beads around the necklace counts as the same necklace), but without flipping over (reversing the order of the beads counts as a different necklace).