Identifier
Values
[1,0] => [1] => [1] => [1] => 0
[1,0,1,0] => [2,1] => [1,2] => [1,2] => 0
[1,1,0,0] => [1,2] => [2,1] => [2,1] => 1
[1,0,1,0,1,0] => [2,3,1] => [1,2,3] => [1,2,3] => 0
[1,0,1,1,0,0] => [2,1,3] => [1,3,2] => [1,3,2] => 1
[1,1,0,0,1,0] => [1,3,2] => [3,2,1] => [3,2,1] => 1
[1,1,0,1,0,0] => [3,1,2] => [3,1,2] => [3,1,2] => 2
[1,1,1,0,0,0] => [1,2,3] => [2,3,1] => [2,3,1] => 1
[1,0,1,0,1,0,1,0] => [2,3,4,1] => [1,2,3,4] => [1,2,3,4] => 0
[1,0,1,0,1,1,0,0] => [2,3,1,4] => [1,2,4,3] => [1,2,4,3] => 1
[1,0,1,1,0,0,1,0] => [2,1,4,3] => [1,4,3,2] => [1,4,3,2] => 1
[1,0,1,1,0,1,0,0] => [2,4,1,3] => [1,4,2,3] => [1,4,2,3] => 2
[1,0,1,1,1,0,0,0] => [2,1,3,4] => [1,3,4,2] => [1,3,4,2] => 1
[1,1,0,0,1,0,1,0] => [1,3,4,2] => [4,2,3,1] => [4,2,3,1] => 1
[1,1,0,0,1,1,0,0] => [1,3,2,4] => [3,2,4,1] => [3,2,4,1] => 1
[1,1,0,1,0,0,1,0] => [3,1,4,2] => [4,1,3,2] => [4,1,3,2] => 2
[1,1,0,1,0,1,0,0] => [3,4,1,2] => [4,1,2,3] => [4,1,2,3] => 3
[1,1,0,1,1,0,0,0] => [3,1,2,4] => [3,1,4,2] => [3,1,4,2] => 2
[1,1,1,0,0,0,1,0] => [1,2,4,3] => [2,4,3,1] => [2,4,3,1] => 1
[1,1,1,0,0,1,0,0] => [1,4,2,3] => [3,4,2,1] => [3,4,2,1] => 2
[1,1,1,0,1,0,0,0] => [4,1,2,3] => [3,4,1,2] => [3,4,1,2] => 2
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [2,3,4,1] => [2,3,4,1] => 1
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Description
The number of preferred parking spots in a parking function less than the index of the car.
Let $(a_1,\dots,a_n)$ be a parking function. Then this statistic returns the number of indices $1\leq i\leq n$ such that $a_i < i$.
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
Map
Inverse Kreweras complement
Description
Sends the permutation $\pi \in \mathfrak{S}_n$ to the permutation $c\pi^{-1}$ where $c = (1,\ldots,n)$ is the long cycle.
Map
parking function
Description
Interpret the permutation as a parking function.