Describe an application of the Burnside Lemma

Asked Jun 29 '21 at 15:45

Active Jun 29 '21 at 15:45

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I would really like to know of an application or an example of the Burnside Lemma which might be not that hard and which is not the usual coloring of parts(edges,vertices etc) of a polytope whith which usually Burnside´s Lemma is shown. Is there any interesting one?

Thanks in advance

asked Jun 29 '21 at 15:45

Annalisa

I guess counting the number of irreducible monic polynomials of degree $n$ over a finite field could be formulated as an application of Burnside even though more often than not it is done by inclusion/exclusion (leading to Möbius inversion) – Jyrki Lahtonen Jun 29 '21 at 16:12
I enjoyed counting Settlers of Catan boards. – Mark S. Jun 29 '21 at 22:26

Describe an application of the Burnside Lemma

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