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Identifier

Mp00041: Integer compositions —conjugate⟶ Integer compositions

Images

[] => []

[1] => [1]

[1,1] => [2]

[2] => [1,1]

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

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

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

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

[1,1,1,1] => [4]

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

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

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

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

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

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

[4] => [1,1,1,1]

[1,1,1,1,1] => [5]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[5] => [1,1,1,1,1]

[1,1,1,1,1,1] => [6]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[6] => [1,1,1,1,1,1]

[1,1,1,1,1,1,1] => [7]

[1,1,1,1,1,2] => [1,6]

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

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

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

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

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

[1,1,1,4] => [1,1,1,4]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[1,6] => [1,1,1,1,1,2]

[2,1,1,1,1,1] => [6,1]

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

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

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

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

>>> Load all 4545 entries. <<<

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

Description

The conjugate of a composition.
The conjugate of a composition

$C$ is defined as the complement (Mp00039complement) of the reversal (Mp00038reverse) of

$C$ .
Equivalently, the ribbon shape corresponding to the conjugate of

$C$ is the conjugate of the ribbon shape of

$C$ .

Properties

bijective, graded, involutive

Sage code

def mapping(elt):
    return elt.conjugate()

Weight

Created

Jan 19, 2020 at 07:28 by FindStatCrew

Updated

Jan 19, 2020 at 07:28 by Martin Rubey