Statements (16)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
gptkb:Cauchy-Frobenius_lemma
|
| gptkbp:appliesTo |
counting distinct colorings
enumeration under symmetry |
| gptkbp:category |
enumerative combinatorics
group actions |
| gptkbp:field |
group theory
combinatorics |
| gptkbp:firstPublished |
1897
|
| gptkbp:form |
|X/G| = (1/|G|) ∑_{g∈G} |Fix(g)|
|
| https://www.w3.org/2000/01/rdf-schema#label |
Burnside's lemma
|
| gptkbp:namedAfter |
gptkb:William_Burnside
|
| gptkbp:state |
The number of orbits of a finite group action on a finite set equals the average number of points fixed by the group elements.
|
| gptkbp:usedIn |
gptkb:Polya_enumeration_theorem
|
| gptkbp:bfsParent |
gptkb:Group_theory
|
| gptkbp:bfsLayer |
5
|