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Identifier

St001058: Ordered trees ⟶ ℤ

Values

[[]] => 1

[[],[]] => 2

[[[]]] => 1

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

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

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

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

[[[[]]]] => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[],[],[],[],[],[]] => 6

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Description

The breadth of the ordered tree.
This is the maximal number of nodes having the same depth.

References

[1] koalo Term for the maximum number of vertices per depth of a rooted tree MathOverflow:287474

Code

def statistic(T):
    return max(T.node_number_at_depth(i) for i in range(T.depth()))

Created

Dec 01, 2017 at 19:26 by Martin Rubey

Updated

Dec 04, 2017 at 18:38 by Martin Rubey