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Matching statistic: St001905
Mapping
St001905: Parking functions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => 0
[1,1] => 1
[1,2] => 0
[2,1] => 1
[1,1,1] => 2
[1,1,2] => 2
[1,2,1] => 1
[2,1,1] => 2
[1,1,3] => 1
[1,3,1] => 1
[3,1,1] => 2
[1,2,2] => 1
[2,1,2] => 2
[2,2,1] => 1
[1,2,3] => 0
[1,3,2] => 1
[2,1,3] => 1
[2,3,1] => 1
[3,1,2] => 2
[3,2,1] => 1
[1,1,1,1] => 3
[1,1,1,2] => 3
[1,1,2,1] => 3
[1,2,1,1] => 2
[2,1,1,1] => 3
[1,1,1,3] => 3
[1,1,3,1] => 2
[1,3,1,1] => 2
[3,1,1,1] => 3
[1,1,1,4] => 2
[1,1,4,1] => 2
[1,4,1,1] => 2
[4,1,1,1] => 3
[1,1,2,2] => 3
[1,2,1,2] => 2
[1,2,2,1] => 2
[2,1,1,2] => 3
[2,1,2,1] => 3
[2,2,1,1] => 2
[1,1,2,3] => 3
[1,1,3,2] => 2
[1,2,1,3] => 2
[1,2,3,1] => 1
[1,3,1,2] => 2
[1,3,2,1] => 2
[2,1,1,3] => 3
[2,1,3,1] => 2
[2,3,1,1] => 2
[3,1,1,2] => 3
[3,1,2,1] => 3
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 $a_i < i$.