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Identifier

St001937: Parking functions ⟶ ℤ

Values

[1] => 1

[1,1] => 2

[1,2] => 2

[2,1] => 1

[1,1,1] => 3

[1,1,2] => 3

[1,2,1] => 3

[2,1,1] => 2

[1,1,3] => 3

[1,3,1] => 2

[3,1,1] => 2

[1,2,2] => 3

[2,1,2] => 2

[2,2,1] => 1

[1,2,3] => 3

[1,3,2] => 2

[2,1,3] => 1

[2,3,1] => 1

[3,1,2] => 2

[3,2,1] => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[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] => 4

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

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

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

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

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

[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] => 4

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

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

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

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

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

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

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

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

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

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

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

[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] => 4

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Description

The size of the center of a parking function.
The center of a parking function $p_1,\dots,p_n$ is the longest subsequence $a_1,\dots,a_k$ such that $a_i\leq i$.

References

[1] Duarte, R., Guedes de Oliveira, António The number of parking functions with center of a given length arXiv:1611.03707

Code

def statistic(p):
    c = []
    j = 1
    for e in p:
        if e <= j:
            c.append(e)
            j += 1
    return len(c)

Created

Dec 30, 2023 at 10:45 by Martin Rubey

Updated

Dec 30, 2023 at 10:45 by Martin Rubey