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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 (i1,i2,…,ik) is sent to (ik,ik−1,…,i1).