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  "body": "\n## Summary\n\nIn [[combinatorial|0JKW7W7XFR]] mathematics, the **necklace polynomial**, or **Moreau's necklace-counting function,** introduced by (txt), counts the number of distinct necklaces of $n$ colored beads chosen out of $k$ available colors, arranged in a cycle. Unlike the usual problem of [[graph coloring|038YGY0HSC]], 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). This counting function also describes the dimensions in a free Lie algebra and the number of irreducible polynomials over a finite field.\n",
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