Identifier
Values
[1,0] => [1,0] => [2,1] => [2,1] => 1
[1,0,1,0] => [1,1,0,0] => [2,3,1] => [2,3,1] => 1
[1,1,0,0] => [1,0,1,0] => [3,1,2] => [3,1,2] => 1
[1,0,1,0,1,0] => [1,1,1,0,0,0] => [2,3,4,1] => [2,3,4,1] => 1
[1,0,1,1,0,0] => [1,1,0,0,1,0] => [2,4,1,3] => [2,4,1,3] => 1
[1,1,0,0,1,0] => [1,0,1,1,0,0] => [3,1,4,2] => [3,1,4,2] => 2
[1,1,0,1,0,0] => [1,0,1,0,1,0] => [4,1,2,3] => [4,1,2,3] => 1
[1,1,1,0,0,0] => [1,1,0,1,0,0] => [4,3,1,2] => [4,3,1,2] => 2
[] => [] => [1] => [1] => 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
peaks-to-valleys
Description
Return the path that has a valley wherever the original path has a peak of height at least one.
More precisely, the height of a valley in the image is the height of the corresponding peak minus $2$.
This is also (the inverse of) rowmotion on Dyck paths regarded as order ideals in the triangular poset.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
parking function
Description
Interpret the permutation as a parking function.