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Identifier
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
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