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Identifier

St001905: Parking functions ⟶ ℤ

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

[3,2,1,1] => 2

[1,1,2,4] => 2

[1,1,4,2] => 2

[1,2,1,4] => 1

[1,2,4,1] => 1

[1,4,1,2] => 2

[1,4,2,1] => 2

[2,1,1,4] => 2

[2,1,4,1] => 2

[2,4,1,1] => 2

[4,1,1,2] => 3

[4,1,2,1] => 3

[4,2,1,1] => 2

[1,1,3,3] => 2

[1,3,1,3] => 2

[1,3,3,1] => 1

[3,1,1,3] => 3

[3,1,3,1] => 2

[3,3,1,1] => 2

[1,1,3,4] => 1

[1,1,4,3] => 2

[1,3,1,4] => 1

[1,3,4,1] => 1

[1,4,1,3] => 2

[1,4,3,1] => 1

[3,1,1,4] => 2

[3,1,4,1] => 2

[3,4,1,1] => 2

[4,1,1,3] => 3

[4,1,3,1] => 2

[4,3,1,1] => 2

[1,2,2,2] => 2

[2,1,2,2] => 3

[2,2,1,2] => 2

[2,2,2,1] => 2

[1,2,2,3] => 2

[1,2,3,2] => 1

[1,3,2,2] => 2

[2,1,2,3] => 3

[2,1,3,2] => 2

[2,2,1,3] => 2

[2,2,3,1] => 1

[2,3,1,2] => 2

[2,3,2,1] => 2

[3,1,2,2] => 3

[3,2,1,2] => 2

[3,2,2,1] => 2

[1,2,2,4] => 1

[1,2,4,2] => 1

[1,4,2,2] => 2

[2,1,2,4] => 2

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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 $a_i < i$.

Code

def statistic(p):
    return sum(1 for i in range(len(p)) if p[i] < i+1)

Created

Jun 11, 2023 at 16:43 by Martin Rubey

Updated

Jun 11, 2023 at 16:43 by Martin Rubey