- FindStat

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Identifier

St000395: Dyck paths ⟶ ℤ

Values

[1,0] => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[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] => 6

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

[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] => 6

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

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

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

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

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

[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] => 7

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

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

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

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

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

[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] => 6

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

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

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

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

[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] => 7

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

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

[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] => 6

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

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

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

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

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

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

[1,0,1,1,1,0,1,0,1,0,0,0] => 10

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

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Description

The sum of the heights of the peaks of a Dyck path.

References

[1] Feinberg, G., Lee, K.-H. Homogeneous representations of Type A KLR-algebras and Dyck paths arXiv:1505.04075

Code

def statistic(D):
    heights = D.heights()
    return sum( heights[i+1] for i in D.peaks() )

Created

Feb 17, 2016 at 20:33 by Christian Stump

Updated

Feb 21, 2022 at 18:53 by Martin Rubey