Identifier
Identifier
St000006 : Dyck paths ⟶ ℤ
Values
[1,0]
generating graphics...
=> 0
[1,0,1,0]
generating graphics...
=> 1
[1,1,0,0]
generating graphics...
=> 0
[1,0,1,0,1,0]
generating graphics...
=> 3
[1,0,1,1,0,0]
generating graphics...
=> 1
[1,1,0,0,1,0]
generating graphics...
=> 2
[1,1,0,1,0,0]
generating graphics...
=> 1
[1,1,1,0,0,0]
generating graphics...
=> 0
[1,0,1,0,1,0,1,0]
generating graphics...
=> 6
[1,0,1,0,1,1,0,0]
generating graphics...
=> 3
[1,0,1,1,0,0,1,0]
generating graphics...
=> 4
[1,0,1,1,0,1,0,0]
generating graphics...
=> 2
[1,0,1,1,1,0,0,0]
generating graphics...
=> 1
[1,1,0,0,1,0,1,0]
generating graphics...
=> 5
[1,1,0,0,1,1,0,0]
generating graphics...
=> 3
[1,1,0,1,0,0,1,0]
generating graphics...
=> 4
[1,1,0,1,0,1,0,0]
generating graphics...
=> 3
[1,1,0,1,1,0,0,0]
generating graphics...
=> 1
[1,1,1,0,0,0,1,0]
generating graphics...
=> 2
[1,1,1,0,0,1,0,0]
generating graphics...
=> 2
[1,1,1,0,1,0,0,0]
generating graphics...
=> 1
[1,1,1,1,0,0,0,0]
generating graphics...
=> 0
[1,0,1,0,1,0,1,0,1,0]
generating graphics...
=> 10
[1,0,1,0,1,0,1,1,0,0]
generating graphics...
=> 6
[1,0,1,0,1,1,0,0,1,0]
generating graphics...
=> 7
[1,0,1,0,1,1,0,1,0,0]
generating graphics...
=> 4
[1,0,1,0,1,1,1,0,0,0]
generating graphics...
=> 3
[1,0,1,1,0,0,1,0,1,0]
generating graphics...
=> 8
[1,0,1,1,0,0,1,1,0,0]
generating graphics...
=> 5
[1,0,1,1,0,1,0,0,1,0]
generating graphics...
=> 6
[1,0,1,1,0,1,0,1,0,0]
generating graphics...
=> 4
[1,0,1,1,0,1,1,0,0,0]
generating graphics...
=> 2
[1,0,1,1,1,0,0,0,1,0]
generating graphics...
=> 4
[1,0,1,1,1,0,0,1,0,0]
generating graphics...
=> 3
[1,0,1,1,1,0,1,0,0,0]
generating graphics...
=> 2
[1,0,1,1,1,1,0,0,0,0]
generating graphics...
=> 1
[1,1,0,0,1,0,1,0,1,0]
generating graphics...
=> 9
[1,1,0,0,1,0,1,1,0,0]
generating graphics...
=> 6
[1,1,0,0,1,1,0,0,1,0]
generating graphics...
=> 7
[1,1,0,0,1,1,0,1,0,0]
generating graphics...
=> 5
[1,1,0,0,1,1,1,0,0,0]
generating graphics...
=> 3
[1,1,0,1,0,0,1,0,1,0]
generating graphics...
=> 8
[1,1,0,1,0,0,1,1,0,0]
generating graphics...
=> 6
[1,1,0,1,0,1,0,0,1,0]
generating graphics...
=> 7
[1,1,0,1,0,1,0,1,0,0]
generating graphics...
=> 6
[1,1,0,1,0,1,1,0,0,0]
generating graphics...
=> 3
[1,1,0,1,1,0,0,0,1,0]
generating graphics...
=> 4
[1,1,0,1,1,0,0,1,0,0]
generating graphics...
=> 4
[1,1,0,1,1,0,1,0,0,0]
generating graphics...
=> 2
[1,1,0,1,1,1,0,0,0,0]
generating graphics...
=> 1
[1,1,1,0,0,0,1,0,1,0]
generating graphics...
=> 5
[1,1,1,0,0,0,1,1,0,0]
generating graphics...
=> 4
[1,1,1,0,0,1,0,0,1,0]
generating graphics...
=> 5
[1,1,1,0,0,1,0,1,0,0]
generating graphics...
=> 5
[1,1,1,0,0,1,1,0,0,0]
generating graphics...
=> 3
[1,1,1,0,1,0,0,0,1,0]
generating graphics...
=> 3
[1,1,1,0,1,0,0,1,0,0]
generating graphics...
=> 4
[1,1,1,0,1,0,1,0,0,0]
generating graphics...
=> 3
[1,1,1,0,1,1,0,0,0,0]
generating graphics...
=> 1
[1,1,1,1,0,0,0,0,1,0]
generating graphics...
=> 2
[1,1,1,1,0,0,0,1,0,0]
generating graphics...
=> 2
[1,1,1,1,0,0,1,0,0,0]
generating graphics...
=> 2
[1,1,1,1,0,1,0,0,0,0]
generating graphics...
=> 1
[1,1,1,1,1,0,0,0,0,0]
generating graphics...
=> 0
[1,0,1,0,1,0,1,0,1,0,1,0]
generating graphics...
=> 15
[1,0,1,0,1,0,1,0,1,1,0,0]
generating graphics...
=> 10
[1,0,1,0,1,0,1,1,0,0,1,0]
generating graphics...
=> 11
[1,0,1,0,1,0,1,1,0,1,0,0]
generating graphics...
=> 7
[1,0,1,0,1,0,1,1,1,0,0,0]
generating graphics...
=> 6
[1,0,1,0,1,1,0,0,1,0,1,0]
generating graphics...
=> 12
[1,0,1,0,1,1,0,0,1,1,0,0]
generating graphics...
=> 8
[1,0,1,0,1,1,0,1,0,0,1,0]
generating graphics...
=> 9
[1,0,1,0,1,1,0,1,0,1,0,0]
generating graphics...
=> 6
[1,0,1,0,1,1,0,1,1,0,0,0]
generating graphics...
=> 4
[1,0,1,0,1,1,1,0,0,0,1,0]
generating graphics...
=> 7
[1,0,1,0,1,1,1,0,0,1,0,0]
generating graphics...
=> 5
[1,0,1,0,1,1,1,0,1,0,0,0]
generating graphics...
=> 4
[1,0,1,0,1,1,1,1,0,0,0,0]
generating graphics...
=> 3
[1,0,1,1,0,0,1,0,1,0,1,0]
generating graphics...
=> 13
[1,0,1,1,0,0,1,0,1,1,0,0]
generating graphics...
=> 9
[1,0,1,1,0,0,1,1,0,0,1,0]
generating graphics...
=> 10
[1,0,1,1,0,0,1,1,0,1,0,0]
generating graphics...
=> 7
[1,0,1,1,0,0,1,1,1,0,0,0]
generating graphics...
=> 5
[1,0,1,1,0,1,0,0,1,0,1,0]
generating graphics...
=> 11
[1,0,1,1,0,1,0,0,1,1,0,0]
generating graphics...
=> 8
[1,0,1,1,0,1,0,1,0,0,1,0]
generating graphics...
=> 9
[1,0,1,1,0,1,0,1,0,1,0,0]
generating graphics...
=> 7
[1,0,1,1,0,1,0,1,1,0,0,0]
generating graphics...
=> 4
[1,0,1,1,0,1,1,0,0,0,1,0]
generating graphics...
=> 6
[1,0,1,1,0,1,1,0,0,1,0,0]
generating graphics...
=> 5
[1,0,1,1,0,1,1,0,1,0,0,0]
generating graphics...
=> 3
[1,0,1,1,0,1,1,1,0,0,0,0]
generating graphics...
=> 2
[1,0,1,1,1,0,0,0,1,0,1,0]
generating graphics...
=> 8
[1,0,1,1,1,0,0,0,1,1,0,0]
generating graphics...
=> 6
[1,0,1,1,1,0,0,1,0,0,1,0]
generating graphics...
=> 7
[1,0,1,1,1,0,0,1,0,1,0,0]
generating graphics...
=> 6
[1,0,1,1,1,0,0,1,1,0,0,0]
generating graphics...
=> 4
[1,0,1,1,1,0,1,0,0,0,1,0]
generating graphics...
=> 5
[1,0,1,1,1,0,1,0,0,1,0,0]
generating graphics...
=> 5
[1,0,1,1,1,0,1,0,1,0,0,0]
generating graphics...
=> 4
[1,0,1,1,1,0,1,1,0,0,0,0]
generating graphics...
=> 2
[1,0,1,1,1,1,0,0,0,0,1,0]
generating graphics...
=> 4
[1,0,1,1,1,1,0,0,0,1,0,0]
generating graphics...
=> 3
[1,0,1,1,1,1,0,0,1,0,0,0]
generating graphics...
=> 3
[1,0,1,1,1,1,0,1,0,0,0,0]
generating graphics...
=> 2
[1,0,1,1,1,1,1,0,0,0,0,0]
generating graphics...
=> 1
[1,1,0,0,1,0,1,0,1,0,1,0]
generating graphics...
=> 14
[1,1,0,0,1,0,1,0,1,1,0,0]
generating graphics...
=> 10
[1,1,0,0,1,0,1,1,0,0,1,0]
generating graphics...
=> 11
[1,1,0,0,1,0,1,1,0,1,0,0]
generating graphics...
=> 8
[1,1,0,0,1,0,1,1,1,0,0,0]
generating graphics...
=> 6
[1,1,0,0,1,1,0,0,1,0,1,0]
generating graphics...
=> 12
[1,1,0,0,1,1,0,0,1,1,0,0]
generating graphics...
=> 9
[1,1,0,0,1,1,0,1,0,0,1,0]
generating graphics...
=> 10
[1,1,0,0,1,1,0,1,0,1,0,0]
generating graphics...
=> 8
[1,1,0,0,1,1,0,1,1,0,0,0]
generating graphics...
=> 5
[1,1,0,0,1,1,1,0,0,0,1,0]
generating graphics...
=> 7
[1,1,0,0,1,1,1,0,0,1,0,0]
generating graphics...
=> 6
[1,1,0,0,1,1,1,0,1,0,0,0]
generating graphics...
=> 4
[1,1,0,0,1,1,1,1,0,0,0,0]
generating graphics...
=> 3
[1,1,0,1,0,0,1,0,1,0,1,0]
generating graphics...
=> 13
[1,1,0,1,0,0,1,0,1,1,0,0]
generating graphics...
=> 10
[1,1,0,1,0,0,1,1,0,0,1,0]
generating graphics...
=> 11
[1,1,0,1,0,0,1,1,0,1,0,0]
generating graphics...
=> 9
[1,1,0,1,0,0,1,1,1,0,0,0]
generating graphics...
=> 6
[1,1,0,1,0,1,0,0,1,0,1,0]
generating graphics...
=> 12
[1,1,0,1,0,1,0,0,1,1,0,0]
generating graphics...
=> 10
[1,1,0,1,0,1,0,1,0,0,1,0]
generating graphics...
=> 11
[1,1,0,1,0,1,0,1,0,1,0,0]
generating graphics...
=> 10
[1,1,0,1,0,1,0,1,1,0,0,0]
generating graphics...
=> 6
[1,1,0,1,0,1,1,0,0,0,1,0]
generating graphics...
=> 7
[1,1,0,1,0,1,1,0,0,1,0,0]
generating graphics...
=> 7
[1,1,0,1,0,1,1,0,1,0,0,0]
generating graphics...
=> 4
[1,1,0,1,0,1,1,1,0,0,0,0]
generating graphics...
=> 3
[1,1,0,1,1,0,0,0,1,0,1,0]
generating graphics...
=> 8
[1,1,0,1,1,0,0,0,1,1,0,0]
generating graphics...
=> 7
[1,1,0,1,1,0,0,1,0,0,1,0]
generating graphics...
=> 8
[1,1,0,1,1,0,0,1,0,1,0,0]
generating graphics...
=> 8
[1,1,0,1,1,0,0,1,1,0,0,0]
generating graphics...
=> 5
[1,1,0,1,1,0,1,0,0,0,1,0]
generating graphics...
=> 5
[1,1,0,1,1,0,1,0,0,1,0,0]
generating graphics...
=> 6
[1,1,0,1,1,0,1,0,1,0,0,0]
generating graphics...
=> 4
[1,1,0,1,1,0,1,1,0,0,0,0]
generating graphics...
=> 2
[1,1,0,1,1,1,0,0,0,0,1,0]
generating graphics...
=> 4
[1,1,0,1,1,1,0,0,0,1,0,0]
generating graphics...
=> 4
[1,1,0,1,1,1,0,0,1,0,0,0]
generating graphics...
=> 3
[1,1,0,1,1,1,0,1,0,0,0,0]
generating graphics...
=> 2
[1,1,0,1,1,1,1,0,0,0,0,0]
generating graphics...
=> 1
[1,1,1,0,0,0,1,0,1,0,1,0]
generating graphics...
=> 9
[1,1,1,0,0,0,1,0,1,1,0,0]
generating graphics...
=> 7
[1,1,1,0,0,0,1,1,0,0,1,0]
generating graphics...
=> 8
[1,1,1,0,0,0,1,1,0,1,0,0]
generating graphics...
=> 7
[1,1,1,0,0,0,1,1,1,0,0,0]
generating graphics...
=> 5
[1,1,1,0,0,1,0,0,1,0,1,0]
generating graphics...
=> 9
[1,1,1,0,0,1,0,0,1,1,0,0]
generating graphics...
=> 8
[1,1,1,0,0,1,0,1,0,0,1,0]
generating graphics...
=> 9
[1,1,1,0,0,1,0,1,0,1,0,0]
generating graphics...
=> 9
[1,1,1,0,0,1,0,1,1,0,0,0]
generating graphics...
=> 6
[1,1,1,0,0,1,1,0,0,0,1,0]
generating graphics...
=> 6
[1,1,1,0,0,1,1,0,0,1,0,0]
generating graphics...
=> 7
[1,1,1,0,0,1,1,0,1,0,0,0]
generating graphics...
=> 5
[1,1,1,0,0,1,1,1,0,0,0,0]
generating graphics...
=> 3
[1,1,1,0,1,0,0,0,1,0,1,0]
generating graphics...
=> 6
[1,1,1,0,1,0,0,0,1,1,0,0]
generating graphics...
=> 6
[1,1,1,0,1,0,0,1,0,0,1,0]
generating graphics...
=> 7
[1,1,1,0,1,0,0,1,0,1,0,0]
generating graphics...
=> 8
[1,1,1,0,1,0,0,1,1,0,0,0]
generating graphics...
=> 6
[1,1,1,0,1,0,1,0,0,0,1,0]
generating graphics...
=> 5
[1,1,1,0,1,0,1,0,0,1,0,0]
generating graphics...
=> 7
[1,1,1,0,1,0,1,0,1,0,0,0]
generating graphics...
=> 6
[1,1,1,0,1,0,1,1,0,0,0,0]
generating graphics...
=> 3
[1,1,1,0,1,1,0,0,0,0,1,0]
generating graphics...
=> 3
[1,1,1,0,1,1,0,0,0,1,0,0]
generating graphics...
=> 4
[1,1,1,0,1,1,0,0,1,0,0,0]
generating graphics...
=> 4
[1,1,1,0,1,1,0,1,0,0,0,0]
generating graphics...
=> 2
[1,1,1,0,1,1,1,0,0,0,0,0]
generating graphics...
=> 1
[1,1,1,1,0,0,0,0,1,0,1,0]
generating graphics...
=> 5
[1,1,1,1,0,0,0,0,1,1,0,0]
generating graphics...
=> 4
[1,1,1,1,0,0,0,1,0,0,1,0]
generating graphics...
=> 5
[1,1,1,1,0,0,0,1,0,1,0,0]
generating graphics...
=> 5
[1,1,1,1,0,0,0,1,1,0,0,0]
generating graphics...
=> 4
[1,1,1,1,0,0,1,0,0,0,1,0]
generating graphics...
=> 4
[1,1,1,1,0,0,1,0,0,1,0,0]
generating graphics...
=> 5
[1,1,1,1,0,0,1,0,1,0,0,0]
generating graphics...
=> 5
[1,1,1,1,0,0,1,1,0,0,0,0]
generating graphics...
=> 3
[1,1,1,1,0,1,0,0,0,0,1,0]
generating graphics...
=> 3
[1,1,1,1,0,1,0,0,0,1,0,0]
generating graphics...
=> 3
[1,1,1,1,0,1,0,0,1,0,0,0]
generating graphics...
=> 4
[1,1,1,1,0,1,0,1,0,0,0,0]
generating graphics...
=> 3
[1,1,1,1,0,1,1,0,0,0,0,0]
generating graphics...
=> 1
[1,1,1,1,1,0,0,0,0,0,1,0]
generating graphics...
=> 2
[1,1,1,1,1,0,0,0,0,1,0,0]
generating graphics...
=> 2
[1,1,1,1,1,0,0,0,1,0,0,0]
generating graphics...
=> 2
[1,1,1,1,1,0,0,1,0,0,0,0]
generating graphics...
=> 2
[1,1,1,1,1,0,1,0,0,0,0,0]
generating graphics...
=> 1
[1,1,1,1,1,1,0,0,0,0,0,0]
generating graphics...
=> 0
Description
The dinv statistic of a Dyck path.
References
[1] Haglund, J. The $q$,$t$-Catalan numbers and the space of diagonal harmonics MathSciNet:2371044
Code
def statistic(x):
    return x.dinv()
Created
Sep 21, 2011 at 03:34 by Chris Berg
Updated
Jun 01, 2015 at 15:50 by Martin Rubey