- FindStat

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Identifier

St001733: Dyck paths ⟶ ℤ

Values

[1,0] => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[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] => 3

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[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] => 4

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

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

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

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

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

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

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

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

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

[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] => 4

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[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] => 3

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Description

The number of weak left to right maxima of a Dyck path.
A weak left to right maximum is a peak whose height is larger than or equal to the height of all peaks to its
left.

References

[1] Blecher, A., Knopfmacher, A. Left to right maxima in Dyck Paths arXiv:2107.03102

Code

def statistic(D):
    hts = D.heights()
    pks = D.peaks()
    ht = 0
    ct = 0
    for pk in pks:
        if hts[pk+1] >= ht:
            ht = hts[pk+1]
            ct += 1
    return ct

Created

Jul 09, 2021 at 10:39 by Martin Rubey

Updated

Jul 09, 2021 at 10:39 by Martin Rubey