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# VisibleList _ Permutation -- computes the action of a permutation on a list

- Operator: _
- Usage:
    `l_p`
- Inputs:
  - l, a visible list,
  - w, a permutation,
- Outputs:
  - a visible list,

## Description

A permutation $p$ acts on the elements of list by permuting the elements of the list according to the permutation. More precisely, if $L = \{ e_1, \dots, e_k \}$ is a list and $p=(p_1, \dots, p_n)$ is a permutation, then the action is given by $p*L = \{ e_{p(1)}, \dots, e_{p(k)}}$.

The permutation cannot permute more than #l elements.

    i1 : p = permutation {3,1,2,5,4,7,6}

    o1 = Permutation{3, 1, 2, 5, 4, 7, 6}

    o1 : Permutation

    i2 : L = {3,1,2,5,4,6,7}

    o2 = {3, 1, 2, 5, 4, 6, 7}

    o2 : List

    i3 : L_p

    o3 = {2, 3, 1, 4, 5, 7, 6}

    o3 : List

The permutation can be a permutation on less than #l elements.

    i4 : p = permutation {3,1,2,4,5}

    o4 = Permutation{3, 1, 2, 4, 5}

    o4 : Permutation

    i5 : L = {3,1,2,5,4,6,7}

    o5 = {3, 1, 2, 5, 4, 6, 7}

    o5 : List

    i6 : L_p

    o6 = {2, 3, 1, 5, 4, 6, 7}

    o6 : List

## See also

- Permutation * VisibleList -- computes the action of a permutation on a list

## Ways to use this method:

- VisibleList _ Permutation -- computes the action of a permutation on a list

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Permutations/Documentation/operationsDocs.m2:178:0.