- FindStat

Identifier

Mp00038: Integer compositions —reverse⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths

Images

[1] => [1] => [1,0]

[1,1] => [1,1] => [1,0,1,0]

[2] => [2] => [1,1,0,0]

[1,1,1] => [1,1,1] => [1,0,1,0,1,0]

[1,2] => [2,1] => [1,1,0,0,1,0]

[2,1] => [1,2] => [1,0,1,1,0,0]

[3] => [3] => [1,1,1,0,0,0]

[1,1,1,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0]

[1,1,2] => [2,1,1] => [1,1,0,0,1,0,1,0]

[1,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0]

[1,3] => [3,1] => [1,1,1,0,0,0,1,0]

[2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0]

[2,2] => [2,2] => [1,1,0,0,1,1,0,0]

[3,1] => [1,3] => [1,0,1,1,1,0,0,0]

[4] => [4] => [1,1,1,1,0,0,0,0]

[1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0]

[1,1,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]

[1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0]

[1,1,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]

[1,2,1,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0]

[1,2,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]

[1,3,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]

[1,4] => [4,1] => [1,1,1,1,0,0,0,0,1,0]

[2,1,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0]

[2,1,2] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]

[2,2,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]

[2,3] => [3,2] => [1,1,1,0,0,0,1,1,0,0]

[3,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0]

[3,2] => [2,3] => [1,1,0,0,1,1,1,0,0,0]

[4,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0]

[5] => [5] => [1,1,1,1,1,0,0,0,0,0]

[1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0]

[1,1,1,1,2] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0]

[1,1,1,2,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0]

[1,1,1,3] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0]

[1,1,2,1,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0]

[1,1,2,2] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0]

[1,1,3,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0]

[1,1,4] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0]

[1,2,1,1,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0]

[1,2,1,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0]

[1,2,2,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0]

[1,2,3] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0]

[1,3,1,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0]

[1,3,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0]

[1,4,1] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0]

[1,5] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0]

[2,1,1,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0]

[2,1,1,2] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0]

[2,1,2,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0]

[2,1,3] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0]

[2,2,1,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0]

[2,2,2] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0]

[2,3,1] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0]

[2,4] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0]

[3,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0]

[3,1,2] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0]

[3,2,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0]

[3,3] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0]

[4,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0]

[4,2] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0]

[5,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0]

[6] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0]

[1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0]

[1,1,1,1,1,2] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0]

[1,1,1,1,2,1] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0]

[1,1,1,1,3] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0]

[1,1,1,2,1,1] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0]

[1,1,1,2,2] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0]

[1,1,1,3,1] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0]

[1,1,1,4] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0]

[1,1,2,1,1,1] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0]

[1,1,2,1,2] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0]

[1,1,2,2,1] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0]

[1,1,2,3] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0]

[1,1,3,1,1] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0]

[1,1,3,2] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0]

[1,1,4,1] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0]

[1,1,5] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0]

[1,2,1,1,1,1] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0]

[1,2,1,1,2] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0]

[1,2,1,2,1] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0]

[1,2,1,3] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0]

[1,2,2,1,1] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0]

[1,2,2,2] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0]

[1,2,3,1] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0]

[1,2,4] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0]

[1,3,1,1,1] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0]

[1,3,1,2] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0]

[1,3,2,1] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0]

[1,3,3] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0]

[1,4,1,1] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0]

[1,4,2] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0]

[1,5,1] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0]

[1,6] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]

[2,1,1,1,1,1] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0]

[2,1,1,1,2] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0]

[2,1,1,2,1] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0]

[2,1,1,3] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0]

[2,1,2,1,1] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0]

[2,1,2,2] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0]

>>> Load all 1297 entries. <<<

Map

reverse

Description

Return the reversal of a composition.
That is, the composition $(i_1, i_2, \ldots, i_k)$ is sent to $(i_k, i_{k-1}, \ldots, i_1)$.

Map

bounce path

Description

The bounce path determined by an integer composition.