- FindStat

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Identifier

St000874: Dyck paths ⟶ ℤ

Values

[1,0,1,0] => 0

[1,1,0,0] => 1

[1,0,1,0,1,0] => 0

[1,0,1,1,0,0] => 3

[1,1,0,0,1,0] => 1

[1,1,0,1,0,0] => 1

[1,1,1,0,0,0] => 2

[1,0,1,0,1,0,1,0] => 0

[1,0,1,0,1,1,0,0] => 5

[1,0,1,1,0,0,1,0] => 3

[1,0,1,1,0,1,0,0] => 3

[1,0,1,1,1,0,0,0] => 4

[1,1,0,0,1,0,1,0] => 1

[1,1,0,0,1,1,0,0] => 5

[1,1,0,1,0,0,1,0] => 1

[1,1,0,1,0,1,0,0] => 1

[1,1,0,1,1,0,0,0] => 4

[1,1,1,0,0,0,1,0] => 2

[1,1,1,0,0,1,0,0] => 2

[1,1,1,0,1,0,0,0] => 2

[1,1,1,1,0,0,0,0] => 3

[1,0,1,0,1,0,1,0,1,0] => 0

[1,0,1,0,1,0,1,1,0,0] => 7

[1,0,1,0,1,1,0,0,1,0] => 5

[1,0,1,0,1,1,0,1,0,0] => 5

[1,0,1,0,1,1,1,0,0,0] => 6

[1,0,1,1,0,0,1,0,1,0] => 3

[1,0,1,1,0,0,1,1,0,0] => 7

[1,0,1,1,0,1,0,0,1,0] => 3

[1,0,1,1,0,1,0,1,0,0] => 3

[1,0,1,1,0,1,1,0,0,0] => 6

[1,0,1,1,1,0,0,0,1,0] => 4

[1,0,1,1,1,0,0,1,0,0] => 4

[1,0,1,1,1,0,1,0,0,0] => 4

[1,0,1,1,1,1,0,0,0,0] => 5

[1,1,0,0,1,0,1,0,1,0] => 1

[1,1,0,0,1,0,1,1,0,0] => 7

[1,1,0,0,1,1,0,0,1,0] => 5

[1,1,0,0,1,1,0,1,0,0] => 5

[1,1,0,0,1,1,1,0,0,0] => 6

[1,1,0,1,0,0,1,0,1,0] => 1

[1,1,0,1,0,0,1,1,0,0] => 7

[1,1,0,1,0,1,0,0,1,0] => 1

[1,1,0,1,0,1,0,1,0,0] => 1

[1,1,0,1,0,1,1,0,0,0] => 6

[1,1,0,1,1,0,0,0,1,0] => 4

[1,1,0,1,1,0,0,1,0,0] => 4

[1,1,0,1,1,0,1,0,0,0] => 4

[1,1,0,1,1,1,0,0,0,0] => 5

[1,1,1,0,0,0,1,0,1,0] => 2

[1,1,1,0,0,0,1,1,0,0] => 7

[1,1,1,0,0,1,0,0,1,0] => 2

[1,1,1,0,0,1,0,1,0,0] => 2

[1,1,1,0,0,1,1,0,0,0] => 6

[1,1,1,0,1,0,0,0,1,0] => 2

[1,1,1,0,1,0,0,1,0,0] => 2

[1,1,1,0,1,0,1,0,0,0] => 2

[1,1,1,0,1,1,0,0,0,0] => 5

[1,1,1,1,0,0,0,0,1,0] => 3

[1,1,1,1,0,0,0,1,0,0] => 3

[1,1,1,1,0,0,1,0,0,0] => 3

[1,1,1,1,0,1,0,0,0,0] => 3

[1,1,1,1,1,0,0,0,0,0] => 4

[1,0,1,0,1,0,1,0,1,0,1,0] => 0

[1,0,1,0,1,0,1,0,1,1,0,0] => 9

[1,0,1,0,1,0,1,1,0,0,1,0] => 7

[1,0,1,0,1,0,1,1,0,1,0,0] => 7

[1,0,1,0,1,0,1,1,1,0,0,0] => 8

[1,0,1,0,1,1,0,0,1,0,1,0] => 5

[1,0,1,0,1,1,0,0,1,1,0,0] => 9

[1,0,1,0,1,1,0,1,0,0,1,0] => 5

[1,0,1,0,1,1,0,1,0,1,0,0] => 5

[1,0,1,0,1,1,0,1,1,0,0,0] => 8

[1,0,1,0,1,1,1,0,0,0,1,0] => 6

[1,0,1,0,1,1,1,0,0,1,0,0] => 6

[1,0,1,0,1,1,1,0,1,0,0,0] => 6

[1,0,1,0,1,1,1,1,0,0,0,0] => 7

[1,0,1,1,0,0,1,0,1,0,1,0] => 3

[1,0,1,1,0,0,1,0,1,1,0,0] => 9

[1,0,1,1,0,0,1,1,0,0,1,0] => 7

[1,0,1,1,0,0,1,1,0,1,0,0] => 7

[1,0,1,1,0,0,1,1,1,0,0,0] => 8

[1,0,1,1,0,1,0,0,1,0,1,0] => 3

[1,0,1,1,0,1,0,0,1,1,0,0] => 9

[1,0,1,1,0,1,0,1,0,0,1,0] => 3

[1,0,1,1,0,1,0,1,0,1,0,0] => 3

[1,0,1,1,0,1,0,1,1,0,0,0] => 8

[1,0,1,1,0,1,1,0,0,0,1,0] => 6

[1,0,1,1,0,1,1,0,0,1,0,0] => 6

[1,0,1,1,0,1,1,0,1,0,0,0] => 6

[1,0,1,1,0,1,1,1,0,0,0,0] => 7

[1,0,1,1,1,0,0,0,1,0,1,0] => 4

[1,0,1,1,1,0,0,0,1,1,0,0] => 9

[1,0,1,1,1,0,0,1,0,0,1,0] => 4

[1,0,1,1,1,0,0,1,0,1,0,0] => 4

[1,0,1,1,1,0,0,1,1,0,0,0] => 8

[1,0,1,1,1,0,1,0,0,0,1,0] => 4

[1,0,1,1,1,0,1,0,0,1,0,0] => 4

[1,0,1,1,1,0,1,0,1,0,0,0] => 4

[1,0,1,1,1,0,1,1,0,0,0,0] => 7

[1,0,1,1,1,1,0,0,0,0,1,0] => 5

>>> Load all 1200 entries. <<<

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Description

The position of the last double rise in a Dyck path.
If the Dyck path has no double rises, this statistic is $0$.

Code

def statistic(D):
    n = len(D)
    i = 0
    l = -1
    while i < n-1:
        if D[i] == D[i+1] == 1:
            l = i
        i += 1
    return l+1

Created

Jul 01, 2017 at 09:32 by Martin Rubey

Updated

Jul 01, 2017 at 09:32 by Martin Rubey