construct a permutation class
Perm( L )
Perm( LL )
list(posint) : a list of positive integers that forms a permutation of 1..n, for some n
list(list(posint)) : a list of lists of positive integers representing disjoint cycles
A permutation is a bijective mapping from the set1,2,…,n to itself, for some positive integer n.
The set of all such permutations forms the symmetric group of degree n, and subgroups of symmetric groups are permutation groups.
Permutations are typically represented as products of disjoint cycles, each of which is an orbit of the permutation. This is a list of the formc1,c2,…,ck in which each ci is itself a listi1,i2,…,im representing a cycle of the formi1↦i2↦im↦i1 .
The Perm constructor creates a permutation, given a specification of its disjoint cycle structure in the form of a list of lists. You can also use a permutation list, which is just the representation of the permutation as a list L of points in which L[ i ] specifies the image of i under the permutation. In particular, the identity permutation is represented by the expression Perm().
The Permutation Operations in GroupTheory page lists commands that operate on permutation objects and are part of the GroupTheory package.
Note that the non-commutative multiplication operator . can be used to multiply permutations.
a ≔ Perm⁡1,2,3,4,5
a ≔ 1,23,4,5
b ≔ Perm⁡1,3,2,6
b ≔ 1,32,6
In the following examples, the PermDegree() and PermProduct() commands are part of the GroupTheory package. They operate on permutation objects constructed by Perm.
The Perm command was introduced in Maple 17.
For more information on Maple 17 changes, see Updates in Maple 17.
Permutation Operations in GroupTheory
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