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Identifier

St000973: Ordered trees ⟶ ℤ

Values

[[]] => 2

[[],[]] => 2

[[[]]] => 4

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

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

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

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

[[[[]]]] => 6

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

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

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

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

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

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

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

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

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

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

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

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

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

[[[[[]]]]] => 8

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[[[[],[[]]]]] => 7

[[[[[]],[]]]] => 7

[[[[[],[]]]]] => 8

[[[[[[]]]]]] => 10

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Description

The length of the boundary of an ordered tree.
This is the sum of the number of edges to the left most and the right most leaf.

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):
    b = 0
    C = T
    while len(C) > 0:
        C = C[0]
        b += 1
    C = T
    while len(C) > 0:
        C = C[-1]
        b += 1        
    return b

Created

Sep 06, 2017 at 23:23 by Martin Rubey

Updated

Sep 06, 2017 at 23:23 by Martin Rubey