NecklacePolynomial

As of Version 10, most of the functionality of the Combinatorica package is built into the Wolfram System. >>

NecklacePolynomial[n,c,Cyclic]
returns a polynomial in the colors in c whose coefficients represent numbers of ways of coloring an n-bead necklace with colors chosen from c, assuming that two colorings are equivalent if one can be obtained from the other by a rotation.

NecklacePolynomial[n,c,Dihedral]
is different in that it considers two colorings equivalent if one can be obtained from the other by a rotation or a flip or both.

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