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Identifier

St000974: Ordered trees ⟶ ℤ

Values

[[]] => 1

[[],[]] => 0

[[[]]] => 2

[[],[],[]] => 0

[[],[[]]] => 0

[[[]],[]] => 0

[[[],[]]] => 1

[[[[]]]] => 3

[[],[],[],[]] => 0

[[],[],[[]]] => 0

[[],[[]],[]] => 0

[[],[[],[]]] => 0

[[],[[[]]]] => 0

[[[]],[],[]] => 0

[[[]],[[]]] => 0

[[[],[]],[]] => 0

[[[[]]],[]] => 0

[[[],[],[]]] => 1

[[[],[[]]]] => 1

[[[[]],[]]] => 1

[[[[],[]]]] => 2

[[[[[]]]]] => 4

[[],[],[],[],[]] => 0

[[],[],[],[[]]] => 0

[[],[],[[]],[]] => 0

[[],[],[[],[]]] => 0

[[],[],[[[]]]] => 0

[[],[[]],[],[]] => 0

[[],[[]],[[]]] => 0

[[],[[],[]],[]] => 0

[[],[[[]]],[]] => 0

[[],[[],[],[]]] => 0

[[],[[],[[]]]] => 0

[[],[[[]],[]]] => 0

[[],[[[],[]]]] => 0

[[],[[[[]]]]] => 0

[[[]],[],[],[]] => 0

[[[]],[],[[]]] => 0

[[[]],[[]],[]] => 0

[[[]],[[],[]]] => 0

[[[]],[[[]]]] => 0

[[[],[]],[],[]] => 0

[[[[]]],[],[]] => 0

[[[],[]],[[]]] => 0

[[[[]]],[[]]] => 0

[[[],[],[]],[]] => 0

[[[],[[]]],[]] => 0

[[[[]],[]],[]] => 0

[[[[],[]]],[]] => 0

[[[[[]]]],[]] => 0

[[[],[],[],[]]] => 1

[[[],[],[[]]]] => 1

[[[],[[]],[]]] => 1

[[[],[[],[]]]] => 1

[[[],[[[]]]]] => 1

[[[[]],[],[]]] => 1

[[[[]],[[]]]] => 1

[[[[],[]],[]]] => 1

[[[[[]]],[]]] => 1

[[[[],[],[]]]] => 2

[[[[],[[]]]]] => 2

[[[[[]],[]]]] => 2

[[[[[],[]]]]] => 3

[[[[[[]]]]]] => 5

[[],[],[],[],[],[]] => 0

[[],[],[],[],[[]]] => 0

[[],[],[],[[]],[]] => 0

[[],[],[],[[],[]]] => 0

[[],[],[],[[[]]]] => 0

[[],[],[[]],[],[]] => 0

[[],[],[[]],[[]]] => 0

[[],[],[[],[]],[]] => 0

[[],[],[[[]]],[]] => 0

[[],[],[[],[],[]]] => 0

[[],[],[[],[[]]]] => 0

[[],[],[[[]],[]]] => 0

[[],[],[[[],[]]]] => 0

[[],[],[[[[]]]]] => 0

[[],[[]],[],[],[]] => 0

[[],[[]],[],[[]]] => 0

[[],[[]],[[]],[]] => 0

[[],[[]],[[],[]]] => 0

[[],[[]],[[[]]]] => 0

[[],[[],[]],[],[]] => 0

[[],[[[]]],[],[]] => 0

[[],[[],[]],[[]]] => 0

[[],[[[]]],[[]]] => 0

[[],[[],[],[]],[]] => 0

[[],[[],[[]]],[]] => 0

[[],[[[]],[]],[]] => 0

[[],[[[],[]]],[]] => 0

[[],[[[[]]]],[]] => 0

[[],[[],[],[],[]]] => 0

[[],[[],[],[[]]]] => 0

[[],[[],[[]],[]]] => 0

[[],[[],[[],[]]]] => 0

[[],[[],[[[]]]]] => 0

[[],[[[]],[],[]]] => 0

[[],[[[]],[[]]]] => 0

[[],[[[],[]],[]]] => 0

[[],[[[[]]],[]]] => 0

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Description

The length of the trunk of an ordered tree.
This is the length of the path from the root to the first vertex which has not exactly one child.

References

[1] Davenport, D. E., Shapiro, L. W., Pudwell, L. K., Woodson, L. C. The boundary of ordered trees MathSciNet:3355976

Code

def statistic(T):
    t = 0
    while len(T) == 1:
        T = T[0]
        t += 1
    return t

Created

Sep 06, 2017 at 23:28 by Martin Rubey

Updated

Dec 28, 2017 at 15:30 by Martin Rubey