Identifier
Mp00305: Permutations —parking function⟶ Parking functions
Mp00319: Parking functions —to composition⟶ Integer compositions
Mp00038: Integer compositions —reverse⟶ Integer compositions
Images
=>
[1]=>[1]=>[1]=>[1] [1,2]=>[1,2]=>[1,2]=>[2,1] [2,1]=>[2,1]=>[2,1]=>[1,2] [1,2,3]=>[1,2,3]=>[1,2,3]=>[3,2,1] [1,3,2]=>[1,3,2]=>[1,3,2]=>[2,3,1] [2,1,3]=>[2,1,3]=>[2,1,3]=>[3,1,2] [2,3,1]=>[2,3,1]=>[2,3,1]=>[1,3,2] [3,1,2]=>[3,1,2]=>[3,1,2]=>[2,1,3] [3,2,1]=>[3,2,1]=>[3,2,1]=>[1,2,3] [1,2,3,4]=>[1,2,3,4]=>[1,2,3,4]=>[4,3,2,1] [1,2,4,3]=>[1,2,4,3]=>[1,2,4,3]=>[3,4,2,1] [1,3,2,4]=>[1,3,2,4]=>[1,3,2,4]=>[4,2,3,1] [1,3,4,2]=>[1,3,4,2]=>[1,3,4,2]=>[2,4,3,1] [1,4,2,3]=>[1,4,2,3]=>[1,4,2,3]=>[3,2,4,1] [1,4,3,2]=>[1,4,3,2]=>[1,4,3,2]=>[2,3,4,1] [2,1,3,4]=>[2,1,3,4]=>[2,1,3,4]=>[4,3,1,2] [2,1,4,3]=>[2,1,4,3]=>[2,1,4,3]=>[3,4,1,2] [2,3,1,4]=>[2,3,1,4]=>[2,3,1,4]=>[4,1,3,2] [2,3,4,1]=>[2,3,4,1]=>[2,3,4,1]=>[1,4,3,2] [2,4,1,3]=>[2,4,1,3]=>[2,4,1,3]=>[3,1,4,2] [2,4,3,1]=>[2,4,3,1]=>[2,4,3,1]=>[1,3,4,2] [3,1,2,4]=>[3,1,2,4]=>[3,1,2,4]=>[4,2,1,3] [3,1,4,2]=>[3,1,4,2]=>[3,1,4,2]=>[2,4,1,3] [3,2,1,4]=>[3,2,1,4]=>[3,2,1,4]=>[4,1,2,3] [3,2,4,1]=>[3,2,4,1]=>[3,2,4,1]=>[1,4,2,3] [3,4,1,2]=>[3,4,1,2]=>[3,4,1,2]=>[2,1,4,3] [3,4,2,1]=>[3,4,2,1]=>[3,4,2,1]=>[1,2,4,3] [4,1,2,3]=>[4,1,2,3]=>[4,1,2,3]=>[3,2,1,4] [4,1,3,2]=>[4,1,3,2]=>[4,1,3,2]=>[2,3,1,4] [4,2,1,3]=>[4,2,1,3]=>[4,2,1,3]=>[3,1,2,4] [4,2,3,1]=>[4,2,3,1]=>[4,2,3,1]=>[1,3,2,4] [4,3,1,2]=>[4,3,1,2]=>[4,3,1,2]=>[2,1,3,4] [4,3,2,1]=>[4,3,2,1]=>[4,3,2,1]=>[1,2,3,4]
Map
parking function
Description
Interpret the permutation as a parking function.
Map
to composition
Description
Return the parking function interpreted as an integer composition.
Map
reverse
Description
Return the reversal of a composition.
That is, the composition $(i_1, i_2, \ldots, i_k)$ is sent to $(i_k, i_{k-1}, \ldots, i_1)$.