Statements (51)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:theorem
|
| gptkbp:applies_to |
finite groups
|
| gptkbp:field |
gptkb:musical_group
|
| gptkbp:has_applications_in |
gptkb:computer_science
chemistry physics |
| https://www.w3.org/2000/01/rdf-schema#label |
Burnside's theorem
|
| gptkbp:is_applied_in |
symmetry analysis
|
| gptkbp:is_cited_in |
many mathematical papers
|
| gptkbp:is_essential_for |
gptkb:Mathematics
|
| gptkbp:is_part_of |
the study of symmetry
|
| gptkbp:is_related_to |
gptkb:Set
gptkb:symmetric_groups gptkb:Burnside's_lemma Galois theory representation theory graph theory Polya's enumeration theorem combinatorial enumeration combinatorial group theory counting problems algebraic structures group representations algebraic combinatorics theory of invariants theory of group actions symmetry groups combinatorial designs group theory applications theory of combinatorial structures action of groups on sets counting distinct arrangements counting orbits finite combinatorial structures finite group actions fixed points in group actions group actions on finite sets theory of counting orbits theory of fixed points theory of permutations theory of symmetries |
| gptkbp:is_taught_in |
abstract algebra courses
|
| gptkbp:is_used_in |
combinatorics
|
| gptkbp:is_used_to |
count distinct colorings of objects.
|
| gptkbp:named_after |
gptkb:William_Burnside
|
| gptkbp:provides |
count of distinct objects under group action
|
| gptkbp:related_to |
orbit-counting theorem
|
| gptkbp:state |
the number of orbits is the average number of points fixed by group elements.
|
| gptkbp:uses |
group actions
|
| gptkbp:bfsParent |
gptkb:William_Burnside
|
| gptkbp:bfsLayer |
5
|