Identifier
- St001959: Dyck paths ⟶ ℤ
Values
[1,0,1,0] => 1
[1,1,0,0] => 2
[1,0,1,0,1,0] => 1
[1,0,1,1,0,0] => 2
[1,1,0,0,1,0] => 2
[1,1,0,1,0,0] => 4
[1,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,0] => 4
[1,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,0] => 4
[1,1,0,1,0,0,1,0] => 4
[1,1,0,1,0,1,0,0] => 8
[1,1,0,1,1,0,0,0] => 6
[1,1,1,0,0,0,1,0] => 3
[1,1,1,0,0,1,0,0] => 6
[1,1,1,0,1,0,0,0] => 9
[1,1,1,1,0,0,0,0] => 4
[1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0] => 2
[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] => 4
[1,0,1,1,0,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,0] => 8
[1,0,1,1,0,1,1,0,0,0] => 6
[1,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,0,0] => 6
[1,0,1,1,1,0,1,0,0,0] => 9
[1,0,1,1,1,1,0,0,0,0] => 4
[1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,0] => 4
[1,1,0,0,1,1,0,1,0,0] => 8
[1,1,0,0,1,1,1,0,0,0] => 6
[1,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,0,0,1,1,0,0] => 8
[1,1,0,1,0,1,0,0,1,0] => 8
[1,1,0,1,0,1,0,1,0,0] => 16
[1,1,0,1,0,1,1,0,0,0] => 12
[1,1,0,1,1,0,0,0,1,0] => 6
[1,1,0,1,1,0,0,1,0,0] => 12
[1,1,0,1,1,0,1,0,0,0] => 18
[1,1,0,1,1,1,0,0,0,0] => 8
[1,1,1,0,0,0,1,0,1,0] => 3
[1,1,1,0,0,0,1,1,0,0] => 6
[1,1,1,0,0,1,0,0,1,0] => 6
[1,1,1,0,0,1,0,1,0,0] => 12
[1,1,1,0,0,1,1,0,0,0] => 9
[1,1,1,0,1,0,0,0,1,0] => 9
[1,1,1,0,1,0,0,1,0,0] => 18
[1,1,1,0,1,0,1,0,0,0] => 27
[1,1,1,0,1,1,0,0,0,0] => 12
[1,1,1,1,0,0,0,0,1,0] => 4
[1,1,1,1,0,0,0,1,0,0] => 8
[1,1,1,1,0,0,1,0,0,0] => 12
[1,1,1,1,0,1,0,0,0,0] => 16
[1,1,1,1,1,0,0,0,0,0] => 5
[1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => 2
[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] => 8
[1,0,1,0,1,1,0,1,1,0,0,0] => 6
[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] => 6
[1,0,1,0,1,1,1,0,1,0,0,0] => 9
[1,0,1,0,1,1,1,1,0,0,0,0] => 4
[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] => 4
[1,0,1,1,0,0,1,1,0,0,1,0] => 4
[1,0,1,1,0,0,1,1,0,1,0,0] => 8
[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] => 4
[1,0,1,1,0,1,0,0,1,1,0,0] => 8
[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] => 16
[1,0,1,1,0,1,0,1,1,0,0,0] => 12
[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] => 12
[1,0,1,1,0,1,1,0,1,0,0,0] => 18
[1,0,1,1,0,1,1,1,0,0,0,0] => 8
[1,0,1,1,1,0,0,0,1,0,1,0] => 3
[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] => 6
[1,0,1,1,1,0,0,1,0,1,0,0] => 12
[1,0,1,1,1,0,0,1,1,0,0,0] => 9
[1,0,1,1,1,0,1,0,0,0,1,0] => 9
[1,0,1,1,1,0,1,0,0,1,0,0] => 18
[1,0,1,1,1,0,1,0,1,0,0,0] => 27
[1,0,1,1,1,0,1,1,0,0,0,0] => 12
[1,0,1,1,1,1,0,0,0,0,1,0] => 4
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Description
The product of the heights of the peaks of a Dyck path.
References
[1] [mathoverflow:480173]
[2] Sum over all Dyck paths of semilength n of products over all peaks p of y_p, where y_p is the y-coordinate of peak p. OEIS:A258173
[2] Sum over all Dyck paths of semilength n of products over all peaks p of y_p, where y_p is the y-coordinate of peak p. OEIS:A258173
Code
def statistic(D):
return prod(D.heights()[i+1] for i in D.peaks())
Created
Oct 07, 2024 at 09:04 by Martin Rubey
Updated
Oct 07, 2024 at 09:04 by Martin Rubey
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