Permutation representation information

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)...

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...

to its permutation representation. Finite permutations are most often represented as group actions on the set X = {1,2, ..., n}. A permutation in this...

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...

transpositions, it is then called an odd permutation, whereas f is an even permutation. The representation of a permutation as a product of transpositions is...

that ρ(g) is a bijection (or permutation) for all g in G. Thus we may equivalently define a permutation representation to be a group homomorphism from...

isomorphic to A1(8). Remarks: 2G2(32n+1) has a doubly transitive permutation representation on 33(2n+1) + 1 points and acts on a 7-dimensional vector space...

cyclic permutation is a permutation consisting of a single cycle. In some cases, cyclic permutations are referred to as cycles; if a cyclic permutation has...

vertex is PSL2(11), and the stabilizer of an edge is 2×A5. This permutation representation can be constructed implicitly by starting with the subgroup PSL2(11)...

number less than n! to factorial representation, one obtains a sequence of n digits that can be converted to a permutation of n elements in a straightforward...

of G . {\displaystyle G.} The left-regular representation is a special case of the permutation representation by choosing X = G . {\displaystyle X=G.} This...

In mathematical finite group theory, a rank 3 permutation group acts transitively on a set such that the stabilizer of a point has 3 orbits. The study...

entries 0.: 26  An n × n permutation matrix can represent a permutation of n elements. Pre-multiplying an n-row matrix M by a permutation matrix P, forming PM...

PMID 10021741. S2CID 6898505. Eiben, A.E.; Smith, J.E. (2015). "Permutation Representation". Introduction to Evolutionary Computing. Natural Computing Series...

mathematics, a generalized permutation matrix (or monomial matrix) is a matrix with the same nonzero pattern as a permutation matrix, i.e. there is exactly...

of the trivial representation of any subgroup is the permutation representation on the cosets of that subgroup. An induced representation of a one dimensional...

hold. Consider for example the natural representation of the symmetric group Sn in n dimensions by permutation matrices, which is certainly faithful....

or Gebhardt (2000). The smallest faithful permutation representation is a rank 5 permutation representation on 8835156 points with stabilizer G2(5). There...

lines. Different permutations may give rise to the same permutation graph; a given graph has a unique representation (up to permutation symmetry) if it...

representations is that the permutation representation on cosets is the special case of induced representation, in which a representation is induced from a trivial...

In mathematics, a permutation group G acting on a non-empty finite set X is called primitive if G acts transitively on X and the only partitions the G-action...