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Identifier

St000700: Ordered trees ⟶ ℤ

Values

[[]] => 1

[[],[]] => 1

[[[]]] => 2

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

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

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

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

[[[[]]]] => 3

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Description

The protection number of an ordered tree.
This is the minimal distance from the root to a leaf.

References

[1] Heuberger, C., Prodinger, H. Protection Number in Plane Trees arXiv:1702.06816

Code

def statistic(T):
    if len(T) == 0:
        return 0
    else:
        return 1+min(statistic(S) for S in T)

Created

Feb 23, 2017 at 20:14 by Martin Rubey

Updated

Dec 26, 2017 at 12:32 by Martin Rubey