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Identifier

St000413: Ordered trees ⟶ ℤ

Values

[[]] => 1

[[],[]] => 1

[[[]]] => 1

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

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

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

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

[[[[]]]] => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Description

The number of ordered trees with the same underlying unordered tree.

Code

@cached_function
def Ordered_to_Rooted(n):
    return [RootedTree(S) for S in OrderedTrees(n)]

def statistic(tree):
    return Ordered_to_Rooted(tree.node_number()).count(RootedTree(tree))

Created

Feb 25, 2016 at 10:56 by Martin Rubey

Updated

Feb 25, 2016 at 10:56 by Martin Rubey