- FindStat

Identifier

Mp00041: Integer compositions —conjugate⟶ Integer compositions
Mp00040: Integer compositions —to partition⟶ Integer partitions

Images

[1] => [1] => [1]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 2023 entries. <<<

Map

conjugate

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 $C$.

Map

to partition

Description

Sends a composition to the partition obtained by sorting the entries.