Identifier
Identifier
Values
[[]] generating graphics... => 1
[[],[]] generating graphics... => 1
[[[]]] generating graphics... => 2
[[],[],[]] generating graphics... => 1
[[],[[]]] generating graphics... => 2
[[[]],[]] generating graphics... => 2
[[[],[]]] generating graphics... => 2
[[[[]]]] generating graphics... => 3
[[],[],[],[]] generating graphics... => 1
[[],[],[[]]] generating graphics... => 2
[[],[[]],[]] generating graphics... => 2
[[],[[],[]]] generating graphics... => 2
[[],[[[]]]] generating graphics... => 3
[[[]],[],[]] generating graphics... => 2
[[[]],[[]]] generating graphics... => 2
[[[],[]],[]] generating graphics... => 2
[[[[]]],[]] generating graphics... => 3
[[[],[],[]]] generating graphics... => 2
[[[],[[]]]] generating graphics... => 3
[[[[]],[]]] generating graphics... => 3
[[[[],[]]]] generating graphics... => 3
[[[[[]]]]] generating graphics... => 4
[[],[],[],[],[]] generating graphics... => 1
[[],[],[],[[]]] generating graphics... => 2
[[],[],[[]],[]] generating graphics... => 2
[[],[],[[],[]]] generating graphics... => 2
[[],[],[[[]]]] generating graphics... => 3
[[],[[]],[],[]] generating graphics... => 2
[[],[[]],[[]]] generating graphics... => 2
[[],[[],[]],[]] generating graphics... => 2
[[],[[[]]],[]] generating graphics... => 3
[[],[[],[],[]]] generating graphics... => 2
[[],[[],[[]]]] generating graphics... => 3
[[],[[[]],[]]] generating graphics... => 3
[[],[[[],[]]]] generating graphics... => 3
[[],[[[[]]]]] generating graphics... => 4
[[[]],[],[],[]] generating graphics... => 2
[[[]],[],[[]]] generating graphics... => 2
[[[]],[[]],[]] generating graphics... => 2
[[[]],[[],[]]] generating graphics... => 2
[[[]],[[[]]]] generating graphics... => 3
[[[],[]],[],[]] generating graphics... => 2
[[[[]]],[],[]] generating graphics... => 3
[[[],[]],[[]]] generating graphics... => 2
[[[[]]],[[]]] generating graphics... => 3
[[[],[],[]],[]] generating graphics... => 2
[[[],[[]]],[]] generating graphics... => 3
[[[[]],[]],[]] generating graphics... => 3
[[[[],[]]],[]] generating graphics... => 3
[[[[[]]]],[]] generating graphics... => 4
[[[],[],[],[]]] generating graphics... => 2
[[[],[],[[]]]] generating graphics... => 3
[[[],[[]],[]]] generating graphics... => 3
[[[],[[],[]]]] generating graphics... => 3
[[[],[[[]]]]] generating graphics... => 4
[[[[]],[],[]]] generating graphics... => 3
[[[[]],[[]]]] generating graphics... => 3
[[[[],[]],[]]] generating graphics... => 3
[[[[[]]],[]]] generating graphics... => 4
[[[[],[],[]]]] generating graphics... => 3
[[[[],[[]]]]] generating graphics... => 4
[[[[[]],[]]]] generating graphics... => 4
[[[[[],[]]]]] generating graphics... => 4
[[[[[[]]]]]] generating graphics... => 5
[[],[],[],[],[],[]] generating graphics... => 1
[[],[],[],[],[[]]] generating graphics... => 2
[[],[],[],[[]],[]] generating graphics... => 2
[[],[],[],[[],[]]] generating graphics... => 2
[[],[],[],[[[]]]] generating graphics... => 3
[[],[],[[]],[],[]] generating graphics... => 2
[[],[],[[]],[[]]] generating graphics... => 2
[[],[],[[],[]],[]] generating graphics... => 2
[[],[],[[[]]],[]] generating graphics... => 3
[[],[],[[],[],[]]] generating graphics... => 2
[[],[],[[],[[]]]] generating graphics... => 3
[[],[],[[[]],[]]] generating graphics... => 3
[[],[],[[[],[]]]] generating graphics... => 3
[[],[],[[[[]]]]] generating graphics... => 4
[[],[[]],[],[],[]] generating graphics... => 2
[[],[[]],[],[[]]] generating graphics... => 2
[[],[[]],[[]],[]] generating graphics... => 2
[[],[[]],[[],[]]] generating graphics... => 2
[[],[[]],[[[]]]] generating graphics... => 3
[[],[[],[]],[],[]] generating graphics... => 2
[[],[[[]]],[],[]] generating graphics... => 3
[[],[[],[]],[[]]] generating graphics... => 2
[[],[[[]]],[[]]] generating graphics... => 3
[[],[[],[],[]],[]] generating graphics... => 2
[[],[[],[[]]],[]] generating graphics... => 3
[[],[[[]],[]],[]] generating graphics... => 3
[[],[[[],[]]],[]] generating graphics... => 3
[[],[[[[]]]],[]] generating graphics... => 4
[[],[[],[],[],[]]] generating graphics... => 2
[[],[[],[],[[]]]] generating graphics... => 3
[[],[[],[[]],[]]] generating graphics... => 3
[[],[[],[[],[]]]] generating graphics... => 3
[[],[[],[[[]]]]] generating graphics... => 4
[[],[[[]],[],[]]] generating graphics... => 3
[[],[[[]],[[]]]] generating graphics... => 3
[[],[[[],[]],[]]] generating graphics... => 3
[[],[[[[]]],[]]] generating graphics... => 4
[[],[[[],[],[]]]] generating graphics... => 3
[[],[[[],[[]]]]] generating graphics... => 4
[[],[[[[]],[]]]] generating graphics... => 4
[[],[[[[],[]]]]] generating graphics... => 4
[[],[[[[[]]]]]] generating graphics... => 5
[[[]],[],[],[],[]] generating graphics... => 2
[[[]],[],[],[[]]] generating graphics... => 2
[[[]],[],[[]],[]] generating graphics... => 2
[[[]],[],[[],[]]] generating graphics... => 2
[[[]],[],[[[]]]] generating graphics... => 3
[[[]],[[]],[],[]] generating graphics... => 2
[[[]],[[]],[[]]] generating graphics... => 2
[[[]],[[],[]],[]] generating graphics... => 2
[[[]],[[[]]],[]] generating graphics... => 3
[[[]],[[],[],[]]] generating graphics... => 2
[[[]],[[],[[]]]] generating graphics... => 3
[[[]],[[[]],[]]] generating graphics... => 3
[[[]],[[[],[]]]] generating graphics... => 3
[[[]],[[[[]]]]] generating graphics... => 4
[[[],[]],[],[],[]] generating graphics... => 2
[[[[]]],[],[],[]] generating graphics... => 3
[[[],[]],[],[[]]] generating graphics... => 2
[[[[]]],[],[[]]] generating graphics... => 3
[[[],[]],[[]],[]] generating graphics... => 2
[[[[]]],[[]],[]] generating graphics... => 3
[[[],[]],[[],[]]] generating graphics... => 2
[[[],[]],[[[]]]] generating graphics... => 3
[[[[]]],[[],[]]] generating graphics... => 3
[[[[]]],[[[]]]] generating graphics... => 3
[[[],[],[]],[],[]] generating graphics... => 2
[[[],[[]]],[],[]] generating graphics... => 3
[[[[]],[]],[],[]] generating graphics... => 3
[[[[],[]]],[],[]] generating graphics... => 3
[[[[[]]]],[],[]] generating graphics... => 4
[[[],[],[]],[[]]] generating graphics... => 2
[[[],[[]]],[[]]] generating graphics... => 3
[[[[]],[]],[[]]] generating graphics... => 3
[[[[],[]]],[[]]] generating graphics... => 3
[[[[[]]]],[[]]] generating graphics... => 4
[[[],[],[],[]],[]] generating graphics... => 2
[[[],[],[[]]],[]] generating graphics... => 3
[[[],[[]],[]],[]] generating graphics... => 3
[[[],[[],[]]],[]] generating graphics... => 3
[[[],[[[]]]],[]] generating graphics... => 4
[[[[]],[],[]],[]] generating graphics... => 3
[[[[]],[[]]],[]] generating graphics... => 3
[[[[],[]],[]],[]] generating graphics... => 3
[[[[[]]],[]],[]] generating graphics... => 4
[[[[],[],[]]],[]] generating graphics... => 3
[[[[],[[]]]],[]] generating graphics... => 4
[[[[[]],[]]],[]] generating graphics... => 4
[[[[[],[]]]],[]] generating graphics... => 4
[[[[[[]]]]],[]] generating graphics... => 5
[[[],[],[],[],[]]] generating graphics... => 2
[[[],[],[],[[]]]] generating graphics... => 3
[[[],[],[[]],[]]] generating graphics... => 3
[[[],[],[[],[]]]] generating graphics... => 3
[[[],[],[[[]]]]] generating graphics... => 4
[[[],[[]],[],[]]] generating graphics... => 3
[[[],[[]],[[]]]] generating graphics... => 3
[[[],[[],[]],[]]] generating graphics... => 3
[[[],[[[]]],[]]] generating graphics... => 4
[[[],[[],[],[]]]] generating graphics... => 3
[[[],[[],[[]]]]] generating graphics... => 4
[[[],[[[]],[]]]] generating graphics... => 4
[[[],[[[],[]]]]] generating graphics... => 4
[[[],[[[[]]]]]] generating graphics... => 5
[[[[]],[],[],[]]] generating graphics... => 3
[[[[]],[],[[]]]] generating graphics... => 3
[[[[]],[[]],[]]] generating graphics... => 3
[[[[]],[[],[]]]] generating graphics... => 3
[[[[]],[[[]]]]] generating graphics... => 4
[[[[],[]],[],[]]] generating graphics... => 3
[[[[[]]],[],[]]] generating graphics... => 4
[[[[],[]],[[]]]] generating graphics... => 3
[[[[[]]],[[]]]] generating graphics... => 4
[[[[],[],[]],[]]] generating graphics... => 3
[[[[],[[]]],[]]] generating graphics... => 4
[[[[[]],[]],[]]] generating graphics... => 4
[[[[[],[]]],[]]] generating graphics... => 4
[[[[[[]]]],[]]] generating graphics... => 5
[[[[],[],[],[]]]] generating graphics... => 3
[[[[],[],[[]]]]] generating graphics... => 4
[[[[],[[]],[]]]] generating graphics... => 4
[[[[],[[],[]]]]] generating graphics... => 4
[[[[],[[[]]]]]] generating graphics... => 5
[[[[[]],[],[]]]] generating graphics... => 4
[[[[[]],[[]]]]] generating graphics... => 4
[[[[[],[]],[]]]] generating graphics... => 4
[[[[[[]]],[]]]] generating graphics... => 5
[[[[[],[],[]]]]] generating graphics... => 4
[[[[[],[[]]]]]] generating graphics... => 5
[[[[[[]],[]]]]] generating graphics... => 5
[[[[[[],[]]]]]] generating graphics... => 5
[[[[[[[]]]]]]] generating graphics... => 6
click to show generating function       
Description
The depth minus 1 of an ordered tree.
The ordered trees of size $n$ are bijection with the Dyck paths of size $n-1$, and this statistic then corresponds to St000013The height of a Dyck path..
Code
def statistic(t):
    return t.depth()-1
Created
Nov 08, 2013 at 21:04 by Viviane Pons
Updated
Feb 17, 2015 at 21:18 by Martin Rubey