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Identifier
Values
[[]] => 1
[[],[]] => 1
[[[]]] => 2
[[],[],[]] => 1
[[],[[]]] => 2
[[[]],[]] => 2
[[[],[]]] => 2
[[[[]]]] => 3
[[],[],[],[]] => 1
[[],[],[[]]] => 2
[[],[[]],[]] => 2
[[],[[],[]]] => 2
[[],[[[]]]] => 3
[[[]],[],[]] => 2
[[[]],[[]]] => 2
[[[],[]],[]] => 2
[[[[]]],[]] => 3
[[[],[],[]]] => 2
[[[],[[]]]] => 3
[[[[]],[]]] => 3
[[[[],[]]]] => 3
[[[[[]]]]] => 4
[[],[],[],[],[]] => 1
[[],[],[],[[]]] => 2
[[],[],[[]],[]] => 2
[[],[],[[],[]]] => 2
[[],[],[[[]]]] => 3
[[],[[]],[],[]] => 2
[[],[[]],[[]]] => 2
[[],[[],[]],[]] => 2
[[],[[[]]],[]] => 3
[[],[[],[],[]]] => 2
[[],[[],[[]]]] => 3
[[],[[[]],[]]] => 3
[[],[[[],[]]]] => 3
[[],[[[[]]]]] => 4
[[[]],[],[],[]] => 2
[[[]],[],[[]]] => 2
[[[]],[[]],[]] => 2
[[[]],[[],[]]] => 2
[[[]],[[[]]]] => 3
[[[],[]],[],[]] => 2
[[[[]]],[],[]] => 3
[[[],[]],[[]]] => 2
[[[[]]],[[]]] => 3
[[[],[],[]],[]] => 2
[[[],[[]]],[]] => 3
[[[[]],[]],[]] => 3
[[[[],[]]],[]] => 3
[[[[[]]]],[]] => 4
[[[],[],[],[]]] => 2
[[[],[],[[]]]] => 3
[[[],[[]],[]]] => 3
[[[],[[],[]]]] => 3
[[[],[[[]]]]] => 4
[[[[]],[],[]]] => 3
[[[[]],[[]]]] => 3
[[[[],[]],[]]] => 3
[[[[[]]],[]]] => 4
[[[[],[],[]]]] => 3
[[[[],[[]]]]] => 4
[[[[[]],[]]]] => 4
[[[[[],[]]]]] => 4
[[[[[[]]]]]] => 5
[[],[],[],[],[],[]] => 1
[[],[],[],[],[[]]] => 2
[[],[],[],[[]],[]] => 2
[[],[],[],[[],[]]] => 2
[[],[],[],[[[]]]] => 3
[[],[],[[]],[],[]] => 2
[[],[],[[]],[[]]] => 2
[[],[],[[],[]],[]] => 2
[[],[],[[[]]],[]] => 3
[[],[],[[],[],[]]] => 2
[[],[],[[],[[]]]] => 3
[[],[],[[[]],[]]] => 3
[[],[],[[[],[]]]] => 3
[[],[],[[[[]]]]] => 4
[[],[[]],[],[],[]] => 2
[[],[[]],[],[[]]] => 2
[[],[[]],[[]],[]] => 2
[[],[[]],[[],[]]] => 2
[[],[[]],[[[]]]] => 3
[[],[[],[]],[],[]] => 2
[[],[[[]]],[],[]] => 3
[[],[[],[]],[[]]] => 2
[[],[[[]]],[[]]] => 3
[[],[[],[],[]],[]] => 2
[[],[[],[[]]],[]] => 3
[[],[[[]],[]],[]] => 3
[[],[[[],[]]],[]] => 3
[[],[[[[]]]],[]] => 4
[[],[[],[],[],[]]] => 2
[[],[[],[],[[]]]] => 3
[[],[[],[[]],[]]] => 3
[[],[[],[[],[]]]] => 3
[[],[[],[[[]]]]] => 4
[[],[[[]],[],[]]] => 3
[[],[[[]],[[]]]] => 3
[[],[[[],[]],[]]] => 3
[[],[[[[]]],[]]] => 4
>>> Load all 196 entries. <<<
[[],[[[],[],[]]]] => 3
[[],[[[],[[]]]]] => 4
[[],[[[[]],[]]]] => 4
[[],[[[[],[]]]]] => 4
[[],[[[[[]]]]]] => 5
[[[]],[],[],[],[]] => 2
[[[]],[],[],[[]]] => 2
[[[]],[],[[]],[]] => 2
[[[]],[],[[],[]]] => 2
[[[]],[],[[[]]]] => 3
[[[]],[[]],[],[]] => 2
[[[]],[[]],[[]]] => 2
[[[]],[[],[]],[]] => 2
[[[]],[[[]]],[]] => 3
[[[]],[[],[],[]]] => 2
[[[]],[[],[[]]]] => 3
[[[]],[[[]],[]]] => 3
[[[]],[[[],[]]]] => 3
[[[]],[[[[]]]]] => 4
[[[],[]],[],[],[]] => 2
[[[[]]],[],[],[]] => 3
[[[],[]],[],[[]]] => 2
[[[[]]],[],[[]]] => 3
[[[],[]],[[]],[]] => 2
[[[[]]],[[]],[]] => 3
[[[],[]],[[],[]]] => 2
[[[],[]],[[[]]]] => 3
[[[[]]],[[],[]]] => 3
[[[[]]],[[[]]]] => 3
[[[],[],[]],[],[]] => 2
[[[],[[]]],[],[]] => 3
[[[[]],[]],[],[]] => 3
[[[[],[]]],[],[]] => 3
[[[[[]]]],[],[]] => 4
[[[],[],[]],[[]]] => 2
[[[],[[]]],[[]]] => 3
[[[[]],[]],[[]]] => 3
[[[[],[]]],[[]]] => 3
[[[[[]]]],[[]]] => 4
[[[],[],[],[]],[]] => 2
[[[],[],[[]]],[]] => 3
[[[],[[]],[]],[]] => 3
[[[],[[],[]]],[]] => 3
[[[],[[[]]]],[]] => 4
[[[[]],[],[]],[]] => 3
[[[[]],[[]]],[]] => 3
[[[[],[]],[]],[]] => 3
[[[[[]]],[]],[]] => 4
[[[[],[],[]]],[]] => 3
[[[[],[[]]]],[]] => 4
[[[[[]],[]]],[]] => 4
[[[[[],[]]]],[]] => 4
[[[[[[]]]]],[]] => 5
[[[],[],[],[],[]]] => 2
[[[],[],[],[[]]]] => 3
[[[],[],[[]],[]]] => 3
[[[],[],[[],[]]]] => 3
[[[],[],[[[]]]]] => 4
[[[],[[]],[],[]]] => 3
[[[],[[]],[[]]]] => 3
[[[],[[],[]],[]]] => 3
[[[],[[[]]],[]]] => 4
[[[],[[],[],[]]]] => 3
[[[],[[],[[]]]]] => 4
[[[],[[[]],[]]]] => 4
[[[],[[[],[]]]]] => 4
[[[],[[[[]]]]]] => 5
[[[[]],[],[],[]]] => 3
[[[[]],[],[[]]]] => 3
[[[[]],[[]],[]]] => 3
[[[[]],[[],[]]]] => 3
[[[[]],[[[]]]]] => 4
[[[[],[]],[],[]]] => 3
[[[[[]]],[],[]]] => 4
[[[[],[]],[[]]]] => 3
[[[[[]]],[[]]]] => 4
[[[[],[],[]],[]]] => 3
[[[[],[[]]],[]]] => 4
[[[[[]],[]],[]]] => 4
[[[[[],[]]],[]]] => 4
[[[[[[]]]],[]]] => 5
[[[[],[],[],[]]]] => 3
[[[[],[],[[]]]]] => 4
[[[[],[[]],[]]]] => 4
[[[[],[[],[]]]]] => 4
[[[[],[[[]]]]]] => 5
[[[[[]],[],[]]]] => 4
[[[[[]],[[]]]]] => 4
[[[[[],[]],[]]]] => 4
[[[[[[]]],[]]]] => 5
[[[[[],[],[]]]]] => 4
[[[[[],[[]]]]]] => 5
[[[[[[]],[]]]]] => 5
[[[[[[],[]]]]]] => 5
[[[[[[[]]]]]]] => 6
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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