Identifier
Values
{{1}} => [1] => [1] => [1] => 0
{{1,2}} => [2,1] => [2,1] => [2,1] => 1
{{1},{2}} => [1,2] => [1,2] => [1,2] => 0
{{1,2,3}} => [2,3,1] => [2,3,1] => [2,3,1] => 1
{{1,2},{3}} => [2,1,3] => [2,1,3] => [2,1,3] => 1
{{1,3},{2}} => [3,2,1] => [3,2,1] => [3,2,1] => 2
{{1},{2,3}} => [1,3,2] => [3,1,2] => [3,1,2] => 1
{{1},{2},{3}} => [1,2,3] => [1,2,3] => [1,2,3] => 0
{{1,2,3,4}} => [2,3,4,1] => [2,3,4,1] => [2,3,4,1] => 1
{{1,2,3},{4}} => [2,3,1,4] => [2,3,1,4] => [2,3,1,4] => 1
{{1,2,4},{3}} => [2,4,3,1] => [4,2,3,1] => [4,2,3,1] => 2
{{1,2},{3,4}} => [2,1,4,3] => [2,4,1,3] => [2,4,1,3] => 1
{{1,2},{3},{4}} => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 1
{{1,3,4},{2}} => [3,2,4,1] => [3,2,4,1] => [3,2,4,1] => 2
{{1,3},{2,4}} => [3,4,1,2] => [3,1,4,2] => [3,1,4,2] => 2
{{1,3},{2},{4}} => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 2
{{1,4},{2,3}} => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 3
{{1},{2,3,4}} => [1,3,4,2] => [3,4,1,2] => [3,4,1,2] => 1
{{1},{2,3},{4}} => [1,3,2,4] => [3,1,2,4] => [3,1,2,4] => 1
{{1,4},{2},{3}} => [4,2,3,1] => [2,4,3,1] => [2,4,3,1] => 2
{{1},{2,4},{3}} => [1,4,3,2] => [4,3,1,2] => [4,3,1,2] => 2
{{1},{2},{3,4}} => [1,2,4,3] => [4,1,2,3] => [4,1,2,3] => 1
{{1},{2},{3},{4}} => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
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Description
The number of descents in a parking function.
This is the number of indices $i$ such that $p_i > p_{i+1}$.
Map
to permutation
Description
Sends the set partition to the permutation obtained by considering the blocks as increasing cycles.
Map
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00067Foata bijection.
Map
parking function
Description
Interpret the permutation as a parking function.