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Identifier
Values
=>
Cc0021;cc-rep
[[]]=>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 [[],[[[],[],[]]]]=>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