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Identifier

Mp00279: Permutations —Backward Rotation⟶ Permutations

Images

[1] => [1]

[1,2] => [2,1]

[2,1] => [1,2]

[1,2,3] => [2,3,1]

[1,3,2] => [3,2,1]

[2,1,3] => [1,3,2]

[2,3,1] => [3,1,2]

[3,1,2] => [1,2,3]

[3,2,1] => [2,1,3]

[1,2,3,4] => [2,3,4,1]

[1,2,4,3] => [2,4,3,1]

[1,3,2,4] => [3,2,4,1]

[1,3,4,2] => [3,4,2,1]

[1,4,2,3] => [4,2,3,1]

[1,4,3,2] => [4,3,2,1]

[2,1,3,4] => [1,3,4,2]

[2,1,4,3] => [1,4,3,2]

[2,3,1,4] => [3,1,4,2]

[2,3,4,1] => [3,4,1,2]

[2,4,1,3] => [4,1,3,2]

[2,4,3,1] => [4,3,1,2]

[3,1,2,4] => [1,2,4,3]

[3,1,4,2] => [1,4,2,3]

[3,2,1,4] => [2,1,4,3]

[3,2,4,1] => [2,4,1,3]

[3,4,1,2] => [4,1,2,3]

[3,4,2,1] => [4,2,1,3]

[4,1,2,3] => [1,2,3,4]

[4,1,3,2] => [1,3,2,4]

[4,2,1,3] => [2,1,3,4]

[4,2,3,1] => [2,3,1,4]

[4,3,1,2] => [3,1,2,4]

[4,3,2,1] => [3,2,1,4]

[1,2,3,4,5] => [2,3,4,5,1]

[1,2,3,5,4] => [2,3,5,4,1]

[1,2,4,3,5] => [2,4,3,5,1]

[1,2,4,5,3] => [2,4,5,3,1]

[1,2,5,3,4] => [2,5,3,4,1]

[1,2,5,4,3] => [2,5,4,3,1]

[1,3,2,4,5] => [3,2,4,5,1]

[1,3,2,5,4] => [3,2,5,4,1]

[1,3,4,2,5] => [3,4,2,5,1]

[1,3,4,5,2] => [3,4,5,2,1]

[1,3,5,2,4] => [3,5,2,4,1]

[1,3,5,4,2] => [3,5,4,2,1]

[1,4,2,3,5] => [4,2,3,5,1]

[1,4,2,5,3] => [4,2,5,3,1]

[1,4,3,2,5] => [4,3,2,5,1]

[1,4,3,5,2] => [4,3,5,2,1]

[1,4,5,2,3] => [4,5,2,3,1]

[1,4,5,3,2] => [4,5,3,2,1]

[1,5,2,3,4] => [5,2,3,4,1]

[1,5,2,4,3] => [5,2,4,3,1]

[1,5,3,2,4] => [5,3,2,4,1]

[1,5,3,4,2] => [5,3,4,2,1]

[1,5,4,2,3] => [5,4,2,3,1]

[1,5,4,3,2] => [5,4,3,2,1]

[2,1,3,4,5] => [1,3,4,5,2]

[2,1,3,5,4] => [1,3,5,4,2]

[2,1,4,3,5] => [1,4,3,5,2]

[2,1,4,5,3] => [1,4,5,3,2]

[2,1,5,3,4] => [1,5,3,4,2]

[2,1,5,4,3] => [1,5,4,3,2]

[2,3,1,4,5] => [3,1,4,5,2]

[2,3,1,5,4] => [3,1,5,4,2]

[2,3,4,1,5] => [3,4,1,5,2]

[2,3,4,5,1] => [3,4,5,1,2]

[2,3,5,1,4] => [3,5,1,4,2]

[2,3,5,4,1] => [3,5,4,1,2]

[2,4,1,3,5] => [4,1,3,5,2]

[2,4,1,5,3] => [4,1,5,3,2]

[2,4,3,1,5] => [4,3,1,5,2]

[2,4,3,5,1] => [4,3,5,1,2]

[2,4,5,1,3] => [4,5,1,3,2]

[2,4,5,3,1] => [4,5,3,1,2]

[2,5,1,3,4] => [5,1,3,4,2]

[2,5,1,4,3] => [5,1,4,3,2]

[2,5,3,1,4] => [5,3,1,4,2]

[2,5,3,4,1] => [5,3,4,1,2]

[2,5,4,1,3] => [5,4,1,3,2]

[2,5,4,3,1] => [5,4,3,1,2]

[3,1,2,4,5] => [1,2,4,5,3]

[3,1,2,5,4] => [1,2,5,4,3]

[3,1,4,2,5] => [1,4,2,5,3]

[3,1,4,5,2] => [1,4,5,2,3]

[3,1,5,2,4] => [1,5,2,4,3]

[3,1,5,4,2] => [1,5,4,2,3]

[3,2,1,4,5] => [2,1,4,5,3]

[3,2,1,5,4] => [2,1,5,4,3]

[3,2,4,1,5] => [2,4,1,5,3]

[3,2,4,5,1] => [2,4,5,1,3]

[3,2,5,1,4] => [2,5,1,4,3]

[3,2,5,4,1] => [2,5,4,1,3]

[3,4,1,2,5] => [4,1,2,5,3]

[3,4,1,5,2] => [4,1,5,2,3]

[3,4,2,1,5] => [4,2,1,5,3]

[3,4,2,5,1] => [4,2,5,1,3]

[3,4,5,1,2] => [4,5,1,2,3]

[3,4,5,2,1] => [4,5,2,1,3]

[3,5,1,2,4] => [5,1,2,4,3]

[3,5,1,4,2] => [5,1,4,2,3]

>>> Load all 5913 entries. <<<

click to show experimental identities (only identities of compositions of up to three maps are shown)

Description

Rotates a permutation by moving the first entry last.
Sends

$\pi(1)\pi(2)\dots\pi(n)$ to

$\pi(2)\pi(3)\dots\pi(n)\pi(1)$ .

Properties

bijective, graded

Sage code

def mapping(pi):
    rot_pi=pi[1:len(pi)]
    rot_pi.append(pi[0])
    return Permutation(rot_pi)

Weight

Created

Jan 09, 2023 at 02:31 by Will Dowling

Updated

Jun 25, 2023 at 00:39 by Nadia Lafreniere