term permutation representation of a (typically finite) group G {\displaystyle G} can refer to either of two closely related notions: a representation of...

mathematics, a permutation group is a group G whose elements are permutations of a given set M and whose group operation is the composition of permutations in G...

Levi-Civita symbol List of permutation topics Major index Permutation category Permutation group Permutation pattern Permutation representation (symmetric group)...

In mathematics, permutation representation may refer to: A group action, see also Permutation representation A representation of a symmetric group (see...

diagrams of size n. Each such irreducible representation can in fact be realized over the integers (every permutation acting by a matrix with integer coefficients);...

a permutation representation it is characterised as having a single orbit and stabilizer the identity subgroup {e} of G. The regular representation of...

abstractly as its permutation representation on four points: V = {\displaystyle V={}} {(), (1,2)(3,4), (1,3)(2,4), (1,4)(2,3)} In this representation, V {\displaystyle...

x=gx} , which has a permutation representation, say ϕ : G → S y m ( G ) {\displaystyle \phi :G\to \mathrm {Sym} (G)} . The representation is faithful if ϕ...

repeated application of the permutation returns to the first number is called a cycle of the permutation. Every permutation can be decomposed into disjoint...

while the third representation (τ) is irreducible. A set-theoretic representation (also known as a group action or permutation representation) of a group...