Statements (57)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:musical_group
|
| gptkbp:bfsLayer |
5
|
| gptkbp:bfsParent |
gptkb:Sporadic_group
|
| gptkbp:class |
for each partition of n
|
| gptkbp:consists_of |
all permutations of n elements
|
| gptkbp:genetic_diversity |
the full symmetric group on n letters
|
| gptkbp:has_color |
for its elements
|
| gptkbp:has_member |
permutation group
alternating group A_n dihedral group D_n symmetric group on fewer elements |
| https://www.w3.org/2000/01/rdf-schema#label |
Symmetric group
|
| gptkbp:is_a |
gptkb:musical_group
|
| gptkbp:is_a_center_for |
trivial for n > 1
|
| gptkbp:is_a_figure_in |
theory of algebraic groups
|
| gptkbp:is_a_source_of |
combinatorial identities
many combinatorial constructions many mathematical problems |
| gptkbp:is_connected_to |
gptkb:television_channel
|
| gptkbp:is_considered_as |
for n > 2
|
| gptkbp:is_fundamental_to |
discrete mathematics
the theory of finite fields |
| gptkbp:is_involved_in |
the classification of finite groups
|
| gptkbp:is_related_to |
graph theory
the theory of modular forms group actions symmetric polynomials the theory of Lie groups the theory of algebraic structures. the theory of algebraic topology the symmetric group on n-1 elements |
| gptkbp:is_represented_in |
permutation matrices
in linear algebra in symmetric functions |
| gptkbp:is_studied_in |
abstract algebra
theory of computation |
| gptkbp:is_used_in |
gptkb:currency
gptkb:legal_case combinatorial problems the study of symmetry combinatorial design the study of algebraic topology the study of coding theory the study of combinatorial optimization |
| gptkbp:key |
Galois theory
representation theory permutation groups finite group theory the theory of algebraic varieties finite simple groups |
| gptkbp:members |
for finite n
|
| gptkbp:order |
n!
|
| gptkbp:produced_by |
transpositions
|
| gptkbp:related_model |
randomized algorithms
permutation-based algorithms |
| gptkbp:significance |
the theory of symmetric functions
|
| gptkbp:was_marked_by |
gptkb:S_n
|