Identifier
Values
[1] => [1] => [1] => 0
[1,2] => [2,1] => [2,1] => 0
[2,1] => [1,2] => [1,2] => 1
[1,2,3] => [3,2,1] => [3,2,1] => 0
[1,3,2] => [3,1,2] => [3,1,2] => 1
[2,1,3] => [2,3,1] => [2,3,1] => 1
[2,3,1] => [2,1,3] => [2,1,3] => 2
[3,1,2] => [1,3,2] => [1,3,2] => 2
[3,2,1] => [1,2,3] => [1,2,3] => 3
[1,2,3,4] => [4,3,2,1] => [4,3,2,1] => 0
[1,2,4,3] => [4,3,1,2] => [4,3,1,2] => 1
[1,3,2,4] => [4,2,3,1] => [4,2,3,1] => 1
[1,3,4,2] => [4,2,1,3] => [4,2,1,3] => 2
[1,4,2,3] => [4,1,3,2] => [4,1,3,2] => 2
[1,4,3,2] => [4,1,2,3] => [4,1,2,3] => 3
[2,1,3,4] => [3,4,2,1] => [3,4,2,1] => 1
[2,1,4,3] => [3,4,1,2] => [3,4,1,2] => 2
[2,3,1,4] => [3,2,4,1] => [3,2,4,1] => 2
[2,3,4,1] => [3,2,1,4] => [3,2,1,4] => 3
[2,4,1,3] => [3,1,4,2] => [3,1,4,2] => 3
[2,4,3,1] => [3,1,2,4] => [3,1,2,4] => 4
[3,1,2,4] => [2,4,3,1] => [2,4,3,1] => 2
[3,1,4,2] => [2,4,1,3] => [2,4,1,3] => 3
[3,2,1,4] => [2,3,4,1] => [2,3,4,1] => 3
[3,2,4,1] => [2,3,1,4] => [2,3,1,4] => 4
[3,4,1,2] => [2,1,4,3] => [2,1,4,3] => 4
[3,4,2,1] => [2,1,3,4] => [2,1,3,4] => 5
[4,1,2,3] => [1,4,3,2] => [1,4,3,2] => 3
[4,1,3,2] => [1,4,2,3] => [1,4,2,3] => 4
[4,2,1,3] => [1,3,4,2] => [1,3,4,2] => 4
[4,2,3,1] => [1,3,2,4] => [1,3,2,4] => 5
[4,3,1,2] => [1,2,4,3] => [1,2,4,3] => 5
[4,3,2,1] => [1,2,3,4] => [1,2,3,4] => 6
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Description
The number of primary dinversion pairs of a labelled dyck path corresponding to a parking function.
Map
complement
Description
Sents a permutation to its complement.
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
Map
parking function
Description
Interpret the permutation as a parking function.