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Perm

construct a permutation class

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

Perm( L )

Perm( LL )

Parameters

L

-

list(posint) : a list of positive integers that forms a permutation of 1..n, for some n

LL

-

 list(list(posint)) : a list of lists of positive integers representing disjoint cycles

Description

• 

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 formi1i2imi1 .

• 

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.

Examples

aPerm1,2,3,4,5

a:=1,23,4,5

(1)

a1

2

(2)

a2

1

(3)

a3

4

(4)

a4

5

(5)

a5

3

(6)

bPerm1,3,2,6

b:=1,32,6

(7)

In the following examples, the PermDegree() and PermProduct() commands are part of the GroupTheory package. They operate on permutation objects constructed by Perm.

withGroupTheory:

PermDegreea

5

(8)

PermDegreeb

6

(9)

PermProducta,b

1,6,2,3,4,5

(10)

Compatibility

• 

The Perm command was introduced in Maple 17.

• 

For more information on Maple 17 changes, see Updates in Maple 17.

See Also

GroupTheory

Permutation Operations in GroupTheory

 


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