Identifier
- St001959: Dyck paths ⟶ ℤ
Values
=>
Cc0005;cc-rep
[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
[1,0,1,1,1,1,0,0,0,1,0,0]=>8
[1,0,1,1,1,1,0,0,1,0,0,0]=>12
[1,0,1,1,1,1,0,1,0,0,0,0]=>16
[1,0,1,1,1,1,1,0,0,0,0,0]=>5
[1,1,0,0,1,0,1,0,1,0,1,0]=>2
[1,1,0,0,1,0,1,0,1,1,0,0]=>4
[1,1,0,0,1,0,1,1,0,0,1,0]=>4
[1,1,0,0,1,0,1,1,0,1,0,0]=>8
[1,1,0,0,1,0,1,1,1,0,0,0]=>6
[1,1,0,0,1,1,0,0,1,0,1,0]=>4
[1,1,0,0,1,1,0,0,1,1,0,0]=>8
[1,1,0,0,1,1,0,1,0,0,1,0]=>8
[1,1,0,0,1,1,0,1,0,1,0,0]=>16
[1,1,0,0,1,1,0,1,1,0,0,0]=>12
[1,1,0,0,1,1,1,0,0,0,1,0]=>6
[1,1,0,0,1,1,1,0,0,1,0,0]=>12
[1,1,0,0,1,1,1,0,1,0,0,0]=>18
[1,1,0,0,1,1,1,1,0,0,0,0]=>8
[1,1,0,1,0,0,1,0,1,0,1,0]=>4
[1,1,0,1,0,0,1,0,1,1,0,0]=>8
[1,1,0,1,0,0,1,1,0,0,1,0]=>8
[1,1,0,1,0,0,1,1,0,1,0,0]=>16
[1,1,0,1,0,0,1,1,1,0,0,0]=>12
[1,1,0,1,0,1,0,0,1,0,1,0]=>8
[1,1,0,1,0,1,0,0,1,1,0,0]=>16
[1,1,0,1,0,1,0,1,0,0,1,0]=>16
[1,1,0,1,0,1,0,1,0,1,0,0]=>32
[1,1,0,1,0,1,0,1,1,0,0,0]=>24
[1,1,0,1,0,1,1,0,0,0,1,0]=>12
[1,1,0,1,0,1,1,0,0,1,0,0]=>24
[1,1,0,1,0,1,1,0,1,0,0,0]=>36
[1,1,0,1,0,1,1,1,0,0,0,0]=>16
[1,1,0,1,1,0,0,0,1,0,1,0]=>6
[1,1,0,1,1,0,0,0,1,1,0,0]=>12
[1,1,0,1,1,0,0,1,0,0,1,0]=>12
[1,1,0,1,1,0,0,1,0,1,0,0]=>24
[1,1,0,1,1,0,0,1,1,0,0,0]=>18
[1,1,0,1,1,0,1,0,0,0,1,0]=>18
[1,1,0,1,1,0,1,0,0,1,0,0]=>36
[1,1,0,1,1,0,1,0,1,0,0,0]=>54
[1,1,0,1,1,0,1,1,0,0,0,0]=>24
[1,1,0,1,1,1,0,0,0,0,1,0]=>8
[1,1,0,1,1,1,0,0,0,1,0,0]=>16
[1,1,0,1,1,1,0,0,1,0,0,0]=>24
[1,1,0,1,1,1,0,1,0,0,0,0]=>32
[1,1,0,1,1,1,1,0,0,0,0,0]=>10
[1,1,1,0,0,0,1,0,1,0,1,0]=>3
[1,1,1,0,0,0,1,0,1,1,0,0]=>6
[1,1,1,0,0,0,1,1,0,0,1,0]=>6
[1,1,1,0,0,0,1,1,0,1,0,0]=>12
[1,1,1,0,0,0,1,1,1,0,0,0]=>9
[1,1,1,0,0,1,0,0,1,0,1,0]=>6
[1,1,1,0,0,1,0,0,1,1,0,0]=>12
[1,1,1,0,0,1,0,1,0,0,1,0]=>12
[1,1,1,0,0,1,0,1,0,1,0,0]=>24
[1,1,1,0,0,1,0,1,1,0,0,0]=>18
[1,1,1,0,0,1,1,0,0,0,1,0]=>9
[1,1,1,0,0,1,1,0,0,1,0,0]=>18
[1,1,1,0,0,1,1,0,1,0,0,0]=>27
[1,1,1,0,0,1,1,1,0,0,0,0]=>12
[1,1,1,0,1,0,0,0,1,0,1,0]=>9
[1,1,1,0,1,0,0,0,1,1,0,0]=>18
[1,1,1,0,1,0,0,1,0,0,1,0]=>18
[1,1,1,0,1,0,0,1,0,1,0,0]=>36
[1,1,1,0,1,0,0,1,1,0,0,0]=>27
[1,1,1,0,1,0,1,0,0,0,1,0]=>27
[1,1,1,0,1,0,1,0,0,1,0,0]=>54
[1,1,1,0,1,0,1,0,1,0,0,0]=>81
[1,1,1,0,1,0,1,1,0,0,0,0]=>36
[1,1,1,0,1,1,0,0,0,0,1,0]=>12
[1,1,1,0,1,1,0,0,0,1,0,0]=>24
[1,1,1,0,1,1,0,0,1,0,0,0]=>36
[1,1,1,0,1,1,0,1,0,0,0,0]=>48
[1,1,1,0,1,1,1,0,0,0,0,0]=>15
[1,1,1,1,0,0,0,0,1,0,1,0]=>4
[1,1,1,1,0,0,0,0,1,1,0,0]=>8
[1,1,1,1,0,0,0,1,0,0,1,0]=>8
[1,1,1,1,0,0,0,1,0,1,0,0]=>16
[1,1,1,1,0,0,0,1,1,0,0,0]=>12
[1,1,1,1,0,0,1,0,0,0,1,0]=>12
[1,1,1,1,0,0,1,0,0,1,0,0]=>24
[1,1,1,1,0,0,1,0,1,0,0,0]=>36
[1,1,1,1,0,0,1,1,0,0,0,0]=>16
[1,1,1,1,0,1,0,0,0,0,1,0]=>16
[1,1,1,1,0,1,0,0,0,1,0,0]=>32
[1,1,1,1,0,1,0,0,1,0,0,0]=>48
[1,1,1,1,0,1,0,1,0,0,0,0]=>64
[1,1,1,1,0,1,1,0,0,0,0,0]=>20
[1,1,1,1,1,0,0,0,0,0,1,0]=>5
[1,1,1,1,1,0,0,0,0,1,0,0]=>10
[1,1,1,1,1,0,0,0,1,0,0,0]=>15
[1,1,1,1,1,0,0,1,0,0,0,0]=>20
[1,1,1,1,1,0,1,0,0,0,0,0]=>25
[1,1,1,1,1,1,0,0,0,0,0,0]=>6
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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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