Identifier
Identifier
St000005: 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... => 3
[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... => 2
[1,1,0,1,0,0,1,0] generating graphics... => 4
[1,1,0,1,0,1,0,0] generating graphics... => 2
[1,1,0,1,1,0,0,0] generating graphics... => 1
[1,1,1,0,0,0,1,0] generating graphics... => 3
[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... => 6
[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... => 4
[1,0,1,1,0,1,0,0,1,0] generating graphics... => 7
[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... => 3
[1,0,1,1,1,0,0,0,1,0] generating graphics... => 5
[1,0,1,1,1,0,0,1,0,0] generating graphics... => 4
[1,0,1,1,1,0,1,0,0,0] generating graphics... => 3
[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... => 5
[1,1,0,0,1,1,0,0,1,0] generating graphics... => 6
[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... => 2
[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... => 4
[1,1,0,1,0,1,0,0,1,0] generating graphics... => 6
[1,1,0,1,0,1,0,1,0,0] generating graphics... => 4
[1,1,0,1,0,1,1,0,0,0] generating graphics... => 2
[1,1,0,1,1,0,0,0,1,0] generating graphics... => 5
[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... => 7
[1,1,1,0,0,0,1,1,0,0] generating graphics... => 3
[1,1,1,0,0,1,0,0,1,0] generating graphics... => 6
[1,1,1,0,0,1,0,1,0,0] generating graphics... => 3
[1,1,1,0,0,1,1,0,0,0] generating graphics... => 2
[1,1,1,0,1,0,0,0,1,0] generating graphics... => 5
[1,1,1,0,1,0,0,1,0,0] generating graphics... => 3
[1,1,1,0,1,0,1,0,0,0] generating graphics... => 2
[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... => 4
[1,1,1,1,0,0,0,1,0,0] generating graphics... => 3
[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... => 10
[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... => 7
[1,0,1,0,1,1,0,1,0,0,1,0] generating graphics... => 11
[1,0,1,0,1,1,0,1,0,1,0,0] generating graphics... => 7
[1,0,1,0,1,1,0,1,1,0,0,0] generating graphics... => 6
[1,0,1,0,1,1,1,0,0,0,1,0] generating graphics... => 8
[1,0,1,0,1,1,1,0,0,1,0,0] generating graphics... => 7
[1,0,1,0,1,1,1,0,1,0,0,0] generating graphics... => 6
[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... => 8
[1,0,1,1,0,0,1,1,0,0,1,0] generating graphics... => 9
[1,0,1,1,0,0,1,1,0,1,0,0] generating graphics... => 8
[1,0,1,1,0,0,1,1,1,0,0,0] generating graphics... => 4
[1,0,1,1,0,1,0,0,1,0,1,0] generating graphics... => 12
[1,0,1,1,0,1,0,0,1,1,0,0] generating graphics... => 7
[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... => 8
[1,0,1,1,0,1,1,0,0,1,0,0] generating graphics... => 7
[1,0,1,1,0,1,1,0,1,0,0,0] generating graphics... => 4
[1,0,1,1,0,1,1,1,0,0,0,0] generating graphics... => 3
[1,0,1,1,1,0,0,0,1,0,1,0] generating graphics... => 10
[1,0,1,1,1,0,0,0,1,1,0,0] generating graphics... => 5
[1,0,1,1,1,0,0,1,0,0,1,0] generating graphics... => 9
[1,0,1,1,1,0,0,1,0,1,0,0] generating graphics... => 5
[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... => 8
[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... => 3
[1,0,1,1,1,1,0,0,0,0,1,0] generating graphics... => 6
[1,0,1,1,1,1,0,0,0,1,0,0] generating graphics... => 5
[1,0,1,1,1,1,0,0,1,0,0,0] generating graphics... => 4
[1,0,1,1,1,1,0,1,0,0,0,0] generating graphics... => 3
[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... => 9
[1,1,0,0,1,0,1,1,0,0,1,0] generating graphics... => 10
[1,1,0,0,1,0,1,1,0,1,0,0] generating graphics... => 9
[1,1,0,0,1,0,1,1,1,0,0,0] generating graphics... => 5
[1,1,0,0,1,1,0,0,1,0,1,0] generating graphics... => 11
[1,1,0,0,1,1,0,0,1,1,0,0] generating graphics... => 6
[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... => 6
[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... => 5
[1,1,0,0,1,1,1,1,0,0,0,0] generating graphics... => 2
[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... => 8
[1,1,0,1,0,0,1,1,0,0,1,0] generating graphics... => 9
[1,1,0,1,0,0,1,1,0,1,0,0] generating graphics... => 8
[1,1,0,1,0,0,1,1,1,0,0,0] generating graphics... => 4
[1,1,0,1,0,1,0,0,1,0,1,0] generating graphics... => 11
[1,1,0,1,0,1,0,0,1,1,0,0] generating graphics... => 6
[1,1,0,1,0,1,0,1,0,0,1,0] generating graphics... => 9
[1,1,0,1,0,1,0,1,0,1,0,0] generating graphics... => 6
[1,1,0,1,0,1,0,1,1,0,0,0] generating graphics... => 4
[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... => 6
[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... => 2
[1,1,0,1,1,0,0,0,1,0,1,0] generating graphics... => 10
[1,1,0,1,1,0,0,0,1,1,0,0] generating graphics... => 5
[1,1,0,1,1,0,0,1,0,0,1,0] generating graphics... => 9
[1,1,0,1,1,0,0,1,0,1,0,0] generating graphics... => 5
[1,1,0,1,1,0,0,1,1,0,0,0] generating graphics... => 4
[1,1,0,1,1,0,1,0,0,0,1,0] generating graphics... => 7
[1,1,0,1,1,0,1,0,0,1,0,0] generating graphics... => 5
[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... => 6
[1,1,0,1,1,1,0,0,0,1,0,0] generating graphics... => 5
[1,1,0,1,1,1,0,0,1,0,0,0] generating graphics... => 4
[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... => 12
[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... => 3
[1,1,1,0,0,1,0,0,1,0,1,0] generating graphics... => 11
[1,1,1,0,0,1,0,0,1,1,0,0] generating graphics... => 6
[1,1,1,0,0,1,0,1,0,0,1,0] generating graphics... => 8
[1,1,1,0,0,1,0,1,0,1,0,0] generating graphics... => 6
[1,1,1,0,0,1,0,1,1,0,0,0] generating graphics... => 3
[1,1,1,0,0,1,1,0,0,0,1,0] generating graphics... => 7
[1,1,1,0,0,1,1,0,0,1,0,0] generating graphics... => 6
[1,1,1,0,0,1,1,0,1,0,0,0] generating graphics... => 3
[1,1,1,0,0,1,1,1,0,0,0,0] generating graphics... => 2
[1,1,1,0,1,0,0,0,1,0,1,0] generating graphics... => 10
[1,1,1,0,1,0,0,0,1,1,0,0] generating graphics... => 5
[1,1,1,0,1,0,0,1,0,0,1,0] generating graphics... => 8
[1,1,1,0,1,0,0,1,0,1,0,0] generating graphics... => 5
[1,1,1,0,1,0,0,1,1,0,0,0] generating graphics... => 3
[1,1,1,0,1,0,1,0,0,0,1,0] generating graphics... => 7
[1,1,1,0,1,0,1,0,0,1,0,0] generating graphics... => 5
[1,1,1,0,1,0,1,0,1,0,0,0] generating graphics... => 3
[1,1,1,0,1,0,1,1,0,0,0,0] generating graphics... => 2
[1,1,1,0,1,1,0,0,0,0,1,0] generating graphics... => 6
[1,1,1,0,1,1,0,0,0,1,0,0] generating graphics... => 5
[1,1,1,0,1,1,0,0,1,0,0,0] generating graphics... => 3
[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... => 9
[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... => 8
[1,1,1,1,0,0,0,1,0,1,0,0] generating graphics... => 4
[1,1,1,1,0,0,0,1,1,0,0,0] generating graphics... => 3
[1,1,1,1,0,0,1,0,0,0,1,0] generating graphics... => 7
[1,1,1,1,0,0,1,0,0,1,0,0] generating graphics... => 4
[1,1,1,1,0,0,1,0,1,0,0,0] generating graphics... => 3
[1,1,1,1,0,0,1,1,0,0,0,0] generating graphics... => 2
[1,1,1,1,0,1,0,0,0,0,1,0] generating graphics... => 6
[1,1,1,1,0,1,0,0,0,1,0,0] generating graphics... => 4
[1,1,1,1,0,1,0,0,1,0,0,0] generating graphics... => 3
[1,1,1,1,0,1,0,1,0,0,0,0] generating graphics... => 2
[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... => 5
[1,1,1,1,1,0,0,0,0,1,0,0] generating graphics... => 4
[1,1,1,1,1,0,0,0,1,0,0,0] generating graphics... => 3
[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
click to show generating function       
Description
The bounce statistic of a Dyck path.
Code
def statistic(x):
    return x.bounce()
Created
Sep 15, 2011 at 15:56 by Chris Berg
Updated
Sep 13, 2014 at 19:29 by Martin Rubey