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.


NecklacePolynomial
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.
Details and Options
- To use NecklacePolynomial, you first need to load the Combinatorica Package using Needs["Combinatorica`"].
See Also
Tech Notes
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Text
Wolfram Research (2012), NecklacePolynomial, Wolfram Language function, https://reference.wolfram.com/language/Combinatorica/ref/NecklacePolynomial.html.
CMS
Wolfram Language. 2012. "NecklacePolynomial." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/Combinatorica/ref/NecklacePolynomial.html.
APA
Wolfram Language. (2012). NecklacePolynomial. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/Combinatorica/ref/NecklacePolynomial.html
BibTeX
@misc{reference.wolfram_2025_necklacepolynomial, author="Wolfram Research", title="{NecklacePolynomial}", year="2012", howpublished="\url{https://reference.wolfram.com/language/Combinatorica/ref/NecklacePolynomial.html}", note=[Accessed: 13-August-2025]}
BibLaTeX
@online{reference.wolfram_2025_necklacepolynomial, organization={Wolfram Research}, title={NecklacePolynomial}, year={2012}, url={https://reference.wolfram.com/language/Combinatorica/ref/NecklacePolynomial.html}, note=[Accessed: 13-August-2025]}