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1999 | OriginalPaper | Buchkapitel

Enumeration by Stabilizer Class

verfasst von : Adalbert Kerber

Erschienen in: Applied Finite Group Actions

Verlag: Springer Berlin Heidelberg

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We now consider another refinement of the Cauchy-Frobenius Lemma. It is due to Burnside, and it allows to enumerate orbits which have a given conjugacy class of subgroups as stabilizers of their elements. For example, it allows us to count the orbits of maximal length |G|, the asymmetric orbits, since these are the orbits ω with trivial stabilizers G x = 1, for each x ∈ ω. A well known formula from Galois theory turns out to be such a number of asymmetric orbits.

Metadaten
Titel
Enumeration by Stabilizer Class
verfasst von
Adalbert Kerber
Copyright-Jahr
1999
Verlag
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-662-11167-3_5