Identifier
Values
[1] => 0
[1,1] => 0
[1,2] => 1
[2,1] => 1
[1,1,1] => 0
[1,1,2] => 1
[1,2,1] => 1
[2,1,1] => 1
[1,1,3] => 2
[1,3,1] => 2
[3,1,1] => 2
[1,2,2] => 2
[2,1,2] => 2
[2,2,1] => 2
[1,2,3] => 3
[1,3,2] => 3
[2,1,3] => 3
[2,3,1] => 3
[3,1,2] => 3
[3,2,1] => 3
[1,1,1,1] => 0
[1,1,1,2] => 1
[1,1,2,1] => 1
[1,2,1,1] => 1
[2,1,1,1] => 1
[1,1,1,3] => 2
[1,1,3,1] => 2
[1,3,1,1] => 2
[3,1,1,1] => 2
[1,1,1,4] => 3
[1,1,4,1] => 3
[1,4,1,1] => 3
[4,1,1,1] => 3
[1,1,2,2] => 2
[1,2,1,2] => 2
[1,2,2,1] => 2
[2,1,1,2] => 2
[2,1,2,1] => 2
[2,2,1,1] => 2
[1,1,2,3] => 3
[1,1,3,2] => 3
[1,2,1,3] => 3
[1,2,3,1] => 3
[1,3,1,2] => 3
[1,3,2,1] => 3
[2,1,1,3] => 3
[2,1,3,1] => 3
[2,3,1,1] => 3
[3,1,1,2] => 3
[3,1,2,1] => 3
[3,2,1,1] => 3
[1,1,2,4] => 4
[1,1,4,2] => 4
[1,2,1,4] => 4
[1,2,4,1] => 4
[1,4,1,2] => 4
[1,4,2,1] => 4
[2,1,1,4] => 4
[2,1,4,1] => 4
[2,4,1,1] => 4
[4,1,1,2] => 4
[4,1,2,1] => 4
[4,2,1,1] => 4
[1,1,3,3] => 4
[1,3,1,3] => 4
[1,3,3,1] => 4
[3,1,1,3] => 4
[3,1,3,1] => 4
[3,3,1,1] => 4
[1,1,3,4] => 5
[1,1,4,3] => 5
[1,3,1,4] => 5
[1,3,4,1] => 5
[1,4,1,3] => 5
[1,4,3,1] => 5
[3,1,1,4] => 5
[3,1,4,1] => 5
[3,4,1,1] => 5
[4,1,1,3] => 5
[4,1,3,1] => 5
[4,3,1,1] => 5
[1,2,2,2] => 3
[2,1,2,2] => 3
[2,2,1,2] => 3
[2,2,2,1] => 3
[1,2,2,3] => 4
[1,2,3,2] => 4
[1,3,2,2] => 4
[2,1,2,3] => 4
[2,1,3,2] => 4
[2,2,1,3] => 4
[2,2,3,1] => 4
[2,3,1,2] => 4
[2,3,2,1] => 4
[3,1,2,2] => 4
[3,2,1,2] => 4
[3,2,2,1] => 4
[1,2,2,4] => 5
[1,2,4,2] => 5
[1,4,2,2] => 5
[2,1,2,4] => 5
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Description
The sum of the entries of a parking function minus its length.
Under the standard map to labelled rooted forests, this statistic is sent to the number of inversions.
Under the standard map to labelled rooted forests, this statistic is sent to the number of inversions.
References
[1] Stanley, R. P. Hyperplane arrangements, parking functions and tree inversions MathSciNet:1627378
Code
def statistic(PF):
return sum(PF) - len(PF)
Created
Jun 26, 2016 at 21:01 by Christian Stump
Updated
Jun 26, 2016 at 21:01 by Christian Stump
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