Applications of Burnside's Formula

Question

The applications of Burnside's formula in counting orbits has wide applications (I believe). But, whatever the books I followed on Group Theory, many (or almost all) of the applications mentioned in them are for "coloring problem" which involves roughly coloring vertices of a regular $n$-gon with different colors.

Q. What are the other simple applications of Burnsides theorem which I can present to undergraduates while teaching group theory?

Counting graphs up to isomorphism (but don't ask me for details). — darij grinberg, Jan 11 '15 at 14:32
See http://math.stackexchange.com/questions/16630/nice-application-of-the-cauchy-frobenius-burnside-p%C3%B3lya-formula — Andreas Caranti, Jan 11 '15 at 14:33
Here's a list of fifty Burnside lemma and Pólya enumeration theorem examples from this site. — MJD, Jan 11 '15 at 14:41
I'd mention to your students this one: https://math.stackexchange.com/a/4609764/1092170 — citadel, Jun 03 '23 at 11:11

score 1 · Answer 1 · edited Apr 13 '17 at 12:19

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If you allow for Polya's enumeration theorem also here are a list of interesting problems that have been answered:

How many ways can you put 8 red, 6 green and 7 blue balls in 4 indistinguishable bins? (A sweet solution by Marko Riedel)

The classical problem of necklaces and braceletets . Also an explanation.

Using it to count graphs (An incredible solution by Marko Riedel)

edited Apr 13 '17 at 12:19

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answered Jan 11 '15 at 16:42

Asinomás

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Applications of Burnside's Formula

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